A story is only good for immersion. If it was good for anything else, developers would be a hell of a lot more involved in it. As it is for most games in the current console generation, the story is just an excuse to go shooting things, or to go solve puzzles. It serves only to satiate a player in the few times he'll ask himself, "Wait, why the hell am I doing this?"
Then you have people like me, who like to be immersed. To me, the ability of a game to have me believe I'm somebody else is paramount. This lets players have an "experience" rather than just playing a game. When you're emotionally connected with the game, the satisfaction of finishing said game is that much sweeter. The prime example, of course, Silent Hill 2, was excellent for this. The story was so immersive that I didn't see the flaws of the combat system or the camera controls, I saw the limitations of the characters.
Braid, from what I have heard, was good, but entirely forgetable.
Never forget, the semblance of a story does not a story make.
Oh and before I forget, Blow is a pretentious git. The sentiment that he seems to be giving of (that games don't particularly need stories) is utterly preposterous.