Ok afterthought... I figured I would elaborate on my take of non-linear vs. linear based story-lines in games.
Linear is essentially a fixed storyline from a games beginning to its end. The player can only follow a fixed storyline - usually in a fixed order of progression, although sometimes linear games contain faux non-linear elements such as allowing the player to choose what to say/ask during dialog conversations or allow the player to try/combine objects with other objects, as & when they like, but usually these elements have no impact on the actual storyline itself.
Non-linear on the other hand, is more complicated because it can come in various forms. Actually I believe non-linear adventure games were pretty popular during the early years of the PC, think text based adventure games back on the old IBM/Acorn machines, which gave you various choices/directions for each scene. I myself have never really played any of them because I didn't get a PC until I was about 11 years old. Most of my youth was spent playing games on consoles & gaming machines, such as: atari, amstrad, amiga, sega, snes etc.
Faux non-linear as I mentioned above is used to give the illusion of player choice when in fact, they choice/action makes no significant changes to the storyline or game world.
Strict non-linear could allow for certain player choices/actions to affect the storyline, characters reactions & game world around you, but these still usually follow a specific order in the games universe. Think TTG as an example as those games choices do impact the world around you but in general you can't really freely explore the game world or play the game in the order you like.
Progressive non-linear - with progressive, being the keyword - would be the same as strict (above) but the world could adapt to more of your choices/actions, you could possibly choose who you want to play as, explore, choose which story branches you wanted to play, or not play & in which order you wanted to play them.
I guess I could mention one other form of non-linear approach to story-telling, which would be procedural based gaming. I'm not very savvy on procedural based games at all, but I think they are very interesting as the games automatically generate the world/storyline based on lots of different factors or by random at the beginning of the game. Essentially you could play a completely different game, each time you pressed new game. Here's a quick example of a procedural indie game that I think worked quite well: "This War of Mine", the game procedurally generated 3 characters at game start, as well as items that could be found in your run down house, the events that occurred during the daytime (who visited, what they wanted) was also unique to each play-through. Also the locations you could visit/raid on each play-through was different. The amount of days/weeks you had to survive was also different on each play-through. You could choose how to approach each situation or whether to run away, give away food, kill or spare someone. Your actions could result in permanent death of your team member or other people. The game was actually pretty tense & atmospheric & kind of reminds me a little of that "gods will be watching" game that was recently mentioned on the portal (pinboard) page, in a way.