I think anyone who is interested in the way games tell stories owes themselves a look at The Stanley Parable. It's not perfect, but it's definitely a delightful way to ponder the concept of game narratives.
It's been touted as a kind of experiment exploring narrative within a virtual world, but structurally it's pretty run-of-the-mill. It uses a basic branching story structure, where each choice the player makes leads to another and so on. Stanley highlights these choices by making the narrator respond to each of them, and nearly all of them result in a wildly different ending to the game. But behind it all this is the exact same build as any multi-path story-driven game.
It's not the structure itself that's interesting, though, but the game's constant self-referencing and breaking of the fourth wall. These underline the game's focus; the conflict between narratives which attempt to tell a story within virtual spaces, and player agency which invariably exists to some degree within these spaces.
The choices and the endings that ensue are a lot of fun, and they all essentially discuss the same thing: the narrative fighting for control with the player. Of course, the game also makes it clear that as long as the player is in the game, she is under the control of the narrative and part of its design.
It's a point I thoroughly support. I think the game tackles gameplay and narrative in one of the best ways I've experienced and raises a lot of questions about the issue. I also think it answers more of these questions than it would care to admit.