I'm going to hone in on some of these unwieldy story structures and identify some of the structural building blocks used in games. And I'm going to do it the best way I how: by talking about a 7-11.
Here's the game scenario:
I want to get to the 7-11, which is a mile away. I can only walk only along one path. Along the way, I'll encounter obstacles and enemies.
This first version is a straightforward linear structure.
Consider some other example structures:
I walk out of my front door, but can go any direction. There are many things for me to do that are fun and adventurous. At some point, I'll learn that there is such a thing as a 7-11, which I may elect to visit, or may never visit.
This is a nonlinear structure.
Halfway between home and the 7-11 is a bridge I need to cross. I go there but it's blocked. I need to find a number of objects, pieces of a code, clues, etc. to be able to get across the bridge.
So I go back and explore my neighborhood, enjoying various adventures, collecting clues, fighting enemies, and polishing my skills. These activities can be done in any order. Eventually I learn, retrieve, or attain whatever I need to get over the bridge.
This is a combination of linear and nonlinear structures.
I have a choice: I can start walking toward the 7-11, but, along the way, there are many side-quests fun adventures I can go on. I can enjoy them in almost any order.
On these side-quests I might get money, weapons, and the like, but if I never did a single side-quest, I could still make it over the bridge. So the side-quests aren't technically necessary.
This is a combination of a linear structure and a different form of nonlinear structures.
I can make it to the 7-11, but laying in wait are a spectrum of enemies and obstacles. I have a wide range of weapons and spells I can use for offensive or defensive purposes, and I must select among them.
Furthermore, I have different styles of making it to the 7-11. For instance, I can sneak there and try to not alert attention. Or I can unleash my firepower and act like the Grim Reaper's bastard stepchild.
This is a multi-mode structure. Almost all games are multi-mode to one degree or another. Sometimes the player can take on different roles, and each role has its own mode (sets of weapons, skills, defenses, etc.).
I can go to the 7-11, but when I come to the bridge, I find that there are actually two bridges, going off in different directions. I have a choice, but they'll both end up at the same place in the end.
This is a combination of linear and multi-path structures. Diverging paths aren't done very often, because this approach requires the creation of up to twice the assets money that could be used for other aspects of the game. Still, some games do have paths that split for a period of time.
As I get toward the 7-11 along a linear path, near the end, I have a choice of which direction to take. One takes me toward the 7-11, and the other takes me to its arch-rival, the notorious Circle-K store.
This is a combination of linear and multi-endgame structures.
I can play the hero or the villain. As the hero, I try to get to the 7-11 and kill the villain. As the villain, I try to kill the hero, and get everyone in a five-square-mile radius to be my slave. As the villain, I can accomplish my goals in a variety of orders.
Examples of emergent gameplay can be found in such highly popular games as Sim City and The Sims. Instead of the game supplying a narrative or a contest (such as with driving games or sports games), emergent games give the player advanced or somewhat "intelligent" building blocks that you can use to create your own story. Did you ever play with Lego™ as a child? It's the same basic concept.
Unlike Lego, in emergent games, there's often some kind of instability built into the system, however. Either you constantly need elements you don't have but are required to get, or the system needs to constantly be attended to so that entropy doesn't destroy it, and so on. Thus, in many games that use emergent gameplay, you're continually prompted to take action to maintain or expand whatever world or system that you've created using the building blocks.
This is a multi-role game; the hero role is linear; the villain mode is nonlinear.
I can make it to the 7-11, fighting all sorts of baddies along the way. There are other missions to run as well. They can be run in any order. Each is a complete adventure unto itself. The missions are only loosely related to each other.
This is a modular structure.
My goal is to build a city, with a happy population and a complex, functioning infrastructure. And, of course, the city will include lots of 7-11s. If you built a city, yours would only vaguely resemble mine.
This is emergent gameplay. And because "The Sims" could have infinite "endings," or no ending at all, games based on emergent gameplay are often called open ended.