Responding to a comment on an old post: some (including me, once) say that "all games are stories" - this stance just muddies the waters about a real conversation you might have been having about story-based games vs. non-story-based games...and you end up having to ask "Okay, just what is a story, anyway?" In Zimmerman's *Rules of Play* they did a pretty good job of separating "emergent narrative" story - the story you might experience playing a game of chess where you come from behind, the game of chess that you tell your friends about - vs. the "color/dressing" story - the backstory, content, theme, symbolism of the pieces, "chess is a story about a war of two armies" story.
The "emergent narrative" story in a game of chess is fundamentally a different kind of storytelling than what a storyteller would call storytelling - and if they are stories, they're usually terribly boring ones - in most games, one player takes a lead and keeps it and wins, and retelling the tale of the game does not enlighten, or have a theme. Maybe one out of a dozen games you get some real drama - the underdog comes from behind, the weak player turns a corner and finds new strength in themselves, whatever. Like life, those moments in games where story emerges are rare. And the rare, say, football game that does have some true drama then gets made into a movie with Mark Wahlberg, where it truly becomes a story in the storytelling sense, where every line of dialog serves some function in the story, but the gaminess is now gone - you know just a little ways into the movie (even if you aren't familiar with sports) that Mark Wahlberg is going to triumph over adversity.
Put another way - a game can be very entertaining to watch - unless you already know the outcome. A story, on the other hand, is worth telling even though the outcome is obvious.
This is the conflict between storiness and gaminess that we wrestle with.