Here's a quote about the difference between stories and games from his book, The Art of Computer Game Design:
… a game is distinguished from a story by the network of options that a game has, as opposed to the single richly-developed thread of a story. Much of the quality of a story is derived from the richness of the information it contains. A story is thus all information and no processing. A game derives its quality from the richness of the network of options it presents. These options are only accessible through the process-intensive aspects of the game. Games that are information-rich and process-poor are closer to stories than to the ideal game.