A statement of function that dictates the parts. The guiding principle by which to draw character, incident, plot. Usually a summary of the opening moments or the generating incident of a story, but not always. In games, a summary that also dictates the type of play. Everyone knows that's Full Throttle.
Good premises are fruitful and suggest all of the above.
Books and movies benefit from built-in pace. Rarely is that possible in a game, where the player dictates the timing of events. A movie plot may resolve happily or unhappily, but it's one or the other. A game almost by definition contains the potential for both success and failure. Murder on the Zinderneuf.