Story is important to some games, not all games. If you're a big fan of, say, Bejeweled Blitz, not a lot of story, Tetris, not a lot of story, great game, really successful. The question - How important is story? - really depends on the type of game you are making. The most important thing to a game is - Is it fun? We'll get to fun in a minute but story adds to fun, story adds to immersion. If you're making an RPG or a story driven game or a virtual reality then story can be exceptionally important. One of the biggest and, you would think, easiest questions is - What makes the game fun? - but it is actually one of the more difficult questions because what is fun? To really know the answer to that question requires a little bit of insight into psychology and many years of wondering the question as a professional game designer. What is fun?