TG: I am wondering if we use the same definition for narrative, and perhaps that muddles the discussion a bit. Normally (at least in film theory) the very simplistic definition of narrative is the combination of plot, characters and story.
Plot here is string of events that make up the narrative, characters the agents in the narrative and story is the overarching environment / backstory for it all. (I have previously used narrative for plot, so have been trying to clean up my terms after that).
Given a game of football (American style or other) you got the basis of the story and characters already laid out by the designers. So what is created dynamically is the plot. However, I would not say that the players creates this themselves, it is rather something that comes to be as matches are played. The dynamics that create these different outcomes are determined by the videogame. And the outcomes cannot be anything, they must lie within the space of possibilities that the videogame set up.
So the designers do not create specifics plot, but they do create a system for certain kinds of plots. This combined with the pre-made story and characters form a narrative that is very much created by designers of the game.
Now players can of course add extra depth to their experience, like dressing the back-story with more details, giving personalities of the various players and so on. But I cannot see how this is different from when reading a book or watching a movie. You can make up all kinds of extra story to vague characters, imagine all actions during cuts, etc. Sure it is a creative act (and videogames can be creative for its audience in a way that no other media can) but it is not the same kind of activity that was used to create the work.
Given the definition I gave above, I do not see that videogame narrative is that much different from other media. The two core differences are that the plot is not set and that the feedback process between medium and audience is far more intricate.
PS. About the "pure game" vs "videogame" discussion you might wanna read this.
JP: I find it strange to argue that the creator might not know the plot, the characters or the setting to their own creation. This to me is much akin to saying that the canvass maker and the paint mixer are really those responsible for a painting.
For, in our hypothetical football game, the Madden player will tell you what characters took part in what plot and in what setting the plot unfolded. This isn't something that the designers or the developers can do.
(As an aside about the utility/thinking behind the whole piece: I would wager a fair amount that when someone finally gets around to slapping electrodes on the skulls of people playing games and compares them with people reading and telling stories, we'll find that the brain activity that occurs when playing games is much more akin to that of telling a story than that of reading one. This to me implies that we need to understand how telling a story affects us psychologically if we want to create better player experiences.)