The reason a story isn't so vital to a game's quality is for one reason, replay value. A story loses much of it's value after you've seen it once. A game however, can still be fun after you've played through it. Maybe it's an increase in difficulty, randomized aspects of gameplay, a different playstyle, or the triumph of defeating another player.
Take Minecraft for example. There isn't any "reason" to the gameplay, yet it's one of the most popular games out there. This is because of the amount of freedom in what you can do, and the tons of different ways you can play the game.