One major aspect of game design concerns the nature of the world that a game is set in. In many cases, this world is linear - meant for direct, story-related interaction, and nothing further. In others, the world may be "open", but the game world still bottlenecks the player at certain intervals to complete story related tasks. In a few games, the entire world acts as part of the gameplay, and everything you do has some sort of consequence. This is easier to achieve in an adaptable system like pen-and-paper gaming than in video games, but there's still a few that have managed to pull it off (to an extent), such as the Way of the Samurai series. Speaking of P&P games, I will also be discussing the Renegade Crowns sourcebook for Warhammer Fantasy Roleplay, which specializes in this kind of design.
Let's start off by establishing some concepts. A "natural" world ought to exist in such a manner that it is functional even if the PC isn't there. It should also have a logic to it that makes sense without the explanation of meta-gaming. This is a point I brought up when discussing cities and facilities - the area should feel like people actually live there, rather than as dressing for a sterile playground. The more realistic it seems, the more meaningful it feels to the player; after all, it's more rewarding to interact with something that feels like actual people doing things than to interact with a lifeless culture. To do this, there's a few things that need to be included.
If the goal of design is to make an area believable, it needs to make sense. This can extend from a geographic level (water flow, geology, forestation and agriculture) to a settled level (the layout and location of towns and villages). In essence, the area should ignore the meta-concepts of "getting the player to go where he needs to go" and exist in a way that makes sense. If it makes sense for a village to be somewhere, it should be there. It's reliant both on physical logic (the way the land itself would develop) and "people logic" (where settlements would be built, how they would use the local geography, and so on).
Obviously, there's going to have to be restrictions on the area at some point - you can't map everything, after all. The best way to do this is to make borders exist in such a way that the player won't really question them. Islands are a good place to start, due to the obvious natural border of the ocean. The important part, though, is the idea that the player shouldn't want to leave - that there should be enough focus on the area itself that they're not bored and trying to find somewhere else to mess around in.
The commentary for Team Fortress 2 stated that all they needed was a guardrail; they were considering ways to make it less obvious (i.e. not having invisible walls), but the playtesters felt that it was unnecessary because they didn't feel constrained by the level design. There was no reason to go out there because the players were focused on the action happening inside the arena. In a game about exploration, on the other hand, the players are going to be trying to find hidden things, and hence a big fake invisible wall is going to feel out of place.
Basically, an area should make sense in its own right. Here's a giant square of land, everything in it makes sense with no artificial barriers or limitations. While the barriers around the area are more arguable, it's not as big of a deal if the area within the barriers is sensible. The more fleshed out and detailed the area is, the more it's going to feel meaningful and the less it's going to feel like taking up space between missions. GTA and its ilk are perfect examples of games that have a lot of space, but not a lot of detail. In contrast, Jagged Alliance 2 lets you explore every single square of the map (and the buildings are sensibly designed). You can't leave the map, but there's no reason to - the map is where the game takes place. It's about keeping the player focused on the area by making the area itself be important instead of pointless filler.
Factions and Inhabitants
Human interaction and habitation is based on some simple principles. People live where it makes sense to live, and they've got specific things they need to survive and thrive. This includes food, water, shelter, and tools, among other things. To realistically depict human infrastructure, every need should be taken care of, or at the very least every object and item should have a source (in terms of resources and in terms of crafting). The creation of a sensible economic system makes the world feel more "real" by providing a source for the items that are used by a given society.
In addition, people respond at least fairly sensibly to other people; if their actions help them, or are in line with their moral code, they like them more. If their actions are harmful or repugnant, then they will dislike them. The problem with most morality systems in games is that it works off of an "objective" concept, rather than representing the cultural and societal values morality represents. Games that avoid the "objective morality" concept generally prefer to work on a faction-based model, which is more sensible. Group A has x values, Group B has y values. If you help Group A, or do things that have x values, Group A likes you more. This is generally the approach that is taken by objective morality as well, except it blatantly divides people into "good" and "evil" if it does it at all (i.e. townsfolk like you if you're good, bandits like you if you're evil).
In "Way of the Samurai 3", there are four factions: the local governor and his troops, the rebels/bandits, the townsfolk, and the villagers. While a normal game might consolidate the townsfolk and villagers into one faction, WotS3 reflects the fact that the two don't exactly like each other despite both being "innocent", and the missions you take for one group will often put you at odds with the other. In addition, people respond naturally in-universe to your positive or negative reputation. When you have a positive reputation, people call out to you as you pass and their speech is much friendlier. When you have a negative reputation, they flee or attack on sight. In this way your status with them is easily understood even without a specific number telling you how friendly you are with them.
In "Renegade Crowns", one of the major aspects of area creation is creating "Princes", i.e. local rulers who control a few towns and villages and serve as the major movers and shakers in the region. This is done through random roll tables determining their archetype, their values, their goals, and so on. The end result is that their followers and courtiers generally follow their example - a knightly lord whose goal is the extermination of all monsters in the area is going to be different than a bandit king who just wants to get rich. This provides a sensible concept for the PCs to interact with: their goals can be made clear through interaction or reputation, and whether the PCs agree with them or not determines their status as an ally, an enemy, or wholly neutral. If the PCs are great crusaders dedicated to stamping out injustice, a cultist or tyrant will be an obvious foe for them to muster their strength against. If the PCs are heretics themselves, they might choose to ally with them, or attempt to usurp their position.
In essence, factions should be treated as people with their own values and identities. If you agree with those values, you'll get along with them. If you don't, you won't. Whether or not the players agree or disagree is dependent on the kind of character they intend to play, and making it so that the players can actually ally with a group that makes sense based on their priorities (or ignore them all, for that matter) is a simple way to give them more choice than the usual "good/evil".
Resources and Interaction
One of the key elements of a believable world is that it is made up of things that can be interacted with. A ubiquitously necessary abstraction in video games is that most of the world is window dressing, not interactive. Simple elements like trees and grass would have various uses in real life, but in video games they're just decoration. Obviously video games can't be faulted for that, with their various technological limitations, but it influences how the player perceives the game world.
The more things that can be interacted with, the more important "the world" is for a scenario. It adds to the player's toolbox, even if it's something simple like grass or water or dirt. It's something that, conceivably, the player could do something with, and it adds to their available plan-constructing resources. Of course, this goes for people as well - if the players need to assemble an army to do something, that army has to come from somewhere. If the players need a specialist for a specific job, that specialist has to be somewhere. No NPC is irrelevant, because they all might have a use (or act against the PCs).
The ultimate goal is to make the environment relevant to what the player is doing, rather than pointless eye-candy. When a village or town is made believable, it means that all the elements within the town make sense, and this encourages the player to make use of those elements if the need arises. In most video games, 90% of the world (at least) would be entirely pointless. In an adaptable tabletop game, nothing has to be. Anything can be used in a given plan, so the players ought to pay attention in case they need things later. The world has more depth when everything in it is interactive, and creative thinking is encouraged when everything can be used.
Essentially, it's about simple principles. Objects in the natural world have values and applications, and making use of those values makes the world feel more real. It's not always plausible for a video game, but in a tabletop game the GM's adaptability makes it much more possible. Like interaction, the goal is to let the player interact with the world in an intuitive fashion. If the player asks "can I do x", and x makes sense for the character to do, they ought to do it. The more the world "makes sense", the more intuitive their decisions can be, and the more they can apply real logic to the situation.
Gameplay and Story
One of the most important elements about this is the elimination of the barrier between gameplay and story. In too many RPGs (computer RPGs, at least), the gameplay exists as filler between stories. Nothing is really accomplished, you just fight random encounters. One of the key points in "Renegade Crowns" is that the number of monsters in an area is limited (although more can come in through various means). This means that if a lair is cleared out, it stays cleared out, and that affects the environment. A local town that's being terrorized by goblins will be safe if the players drive them away. It provides more context for their action and makes combat into a tool, rather than a distraction.
One important thing that the inclusion of factions in games like Way of the Samurai or S.T.A.L.K.E.R. does is make it so that, for the most part, combat has consequences. There's reasons to run from a fight if you're trying to avoid making people more angry at you. If a game is sufficiently difficult, there may even be a reason to surrender (at least if you care about what happens to your character). One thing that I really liked in WotS3 was the inclusion of an "apologize" button: if you drew your sword and offended someone, you could beg their forgiveness and potentially avoid a fight. This isn't a dialogue option, either - it's a natural part of the game world based wholly on simple actions and reactions. Everything you do in the game world can contribute to people's opinions of you, and while the game does eventually "take the reins" and push you along a more linear story (depending on which path you choose to take), the world also develops outside of that.
In essence, if you use stealth in a game, the story should develop as though you weren't detected. One of my pet peeves is games where after a full sequence of sneaking past guards, the player character jumps out of the shadows and talks to someone. You can see this in the trailer for Deus Ex 3 when the "aggressive method" and "stealth method" lead to the same cutscene. It's not rewarding the player for choosing a harder path, because that would be unfair to people who just wanted to shoot things. A similar problem occurred with the Renegade and Paragon choices in Mass Effect - both of them would "get things done", as it were, so all that changed was the method. If the game was unbeatable if you chose all Paragon or all Renegade, that would be unfair to players who liked that particular playstyle. In both DX3 and ME, using the "adaptive" or "neutral" method is kind of pointless, because it just means you're indecisive rather than actually making decisions based on the situation.
Basically, games should base themselves around natural reactions. If you sneak into a place, the game should reflect that. If you avoid killing people, the game should reflect that. The more "linear" and "story-based" a game is, the less opportunities it has to feel like it makes sense. The player isn't rewarded for their choices if the game ends up ignoring them, and if the choice doesn't matter, why did you let the player make it in the first place? Why provide the illusion of free will only to deprive the player as soon as a cutscene begins?
So, To Sum Up:
1) A believable world allows the player to interact with it in an intuitive fashion.
2) The more sensible and believable a world is, the more the player is encouraged to treat it like a real place.
3) Interaction (whether human or environmental) is guided by simple, understandable principles that players can use to their advantage.
4) Creating a situation where a world is "real" eliminates the divide between gameplay and story by making the former affect the latter.