As I've said before, I think the feature that differentiates video games from regular games and sports is the fact that you do not know the rules of a video game in advance. Not all video games are like this, but the thing that makes video games unique is that you are learning the rules of the game on the fly as you move through the environment and work towards surmounting all the challenges the game throws at you. I think that this dynamic gives long-form video games unique narrative possibilities relative to other, non-participatory forms of art, so I'm going to take a shot at explaining how this is so.
My basic idea is that when the player inhabits the role of a protagonist, there are two kinds of progress that are going on in the course of a game
The first is what I'll call gameplay progress. When you begin a game you usually start off with a meager set of capabilities. You usually begin by familiarizing with the basic play mechanics and controls-- how you hit A to jump and push the left thumbstick to move around and pull the right trigger to whale on a chicken.
The Legend of Zelda and Metroid, the Odyssey and Aeneid of console gaming, set the basic template for gameplay progress by tying your access to new parts of the world to your acquisition and mastery of new skills and rules. In Zelda, for example, you acquire one new skill per dungeon, and then you earn the right to move on to the next chunk of the world by using that skill to reach and defeat the dungeon's boss. (I was playing Phantom Hourglass last spring, and by the time it was over felt this formula had become too rigid and had degenerated into mannerism. Don't get me started on the last few Castlevanias.) By the time you finish, both you and your character are more capable than when you began, because you've learned a bunch of new rules. That's progress.
Alongside gameplay progress-- the narrative of your mastery of new skills and capabilities-- there is also the venerable narrative progress native to storytelling. In a story, progress consists of the way its protagonist matures as he goes through the world and is transformed by his new experiences. Literature provides the standard models for this kind of progress. Telemachus begins the Odyssey as a faint-hearted boy tormented by his mother's suitors and ends the epic by helping to vanquish them and claim his birthright. As Huck Finn goes off on his journey up the Mississippi, he becomes caught between a conscience that tells him that slavery is right, and a heart that tells him it's wrong. By making his way through the hazards of river life and becoming friends with Jim he learns which one he should listen to; the moral drama of the novel comes from watching a good heart win out over a bad conscience. These are classic forms of narrative progress: the development of character that transpires as the protagonist is transformed by experience.
Games have unique expressive capabilities because they can superimpose and juxtapose these two distinct forms of progress in the course of their narratives. Games are great at telling coming-of-age stories because the implicit logic of gameplay already tells a story about the player's development towards maturity. Zelda has a purchase on us that outstrips its narrative sophistication because our identification with Link is different from our relationship to a character in a novel: when we begin the game, we are the powerless boy on an island who must learn about the world in order to live up to our destiny. The reason Half-Life 2 is so compelling is that you begin as a faceless nobody and spend the game becoming the efficacious person-- Gordon Freeman-- that you see reflected in the other character's eyes. Bioshock (putatively) offers the player a choice between becoming powerful and becoming morally corrupt, and this choice has significance because the empowerment you are offered is uniquely your own.
I think games have only begun to exploit the narrative possibilities of the empowerment inherent in gameplay progress. In most games we become good by becoming powerful, and while there is much to love about this story there are so many other potential experiences that can be created by playing these two forms of progress against each other, like Bioshock's Faustian bargain. We've seen a many a gaming Bildungsroman that ends in triumph, but we still haven't seen gaming's The Red and The Black. Life and literature abound in stories about the perils of maturity and the ambiguities inherent in our drive to master the world around us. Games can be too.