I don't know. I think story is important in a game, but at the same time if it isn't well executed there's no point. Take Doom 3. There was very minimal story. You go th Mars, bad shit happens, now you have to kill everything and close the gate to hell. Basically, that's it, but it worked, because it gave you a clear cut goal and you knew what you had to do. F.E.A.R. 2, on the other hand, confuses me. I know I was supposed to go after Aristide, but not anymore because... something happened and now she's not important, even though people keep talking about her. And Alma is after me so I have to go to the facility on the island so I can destroy her, but it's never really explained why she's after you, except that you have big psychic powers (which you can't use) and she wants to "devour you". Uh.... And for some reason some guy from your team, Keegan, is trying to find her, which is kind of pointless. And that's as far as I got, since my brain started to hurt. Not to mention my eyes.
The point is, yes story is important, but it's better to have minimal story if you don't kinow what the heck you're doing with it.