They use Story as a sub category for scoring for all their reviews. I don't see why the criteria should change depending on the game. Mario Party may have a shit story, but it could make up it score in presentation, gameplay and sound. I think that's fair.

When a game doesn't have a story they cut out that category, but when one is presented (even if it is just a pretense at the beginning of the game to get into the gameplay) I think it's legitimate to score on it.  And then how that score affects the overall would be based on how much they think the story for better or for worse affected the game as a whole.

edit: and if you look at the scores it was 5.5, 8.2 and 8.6 with an overall of 8.3 so it's obvious the story wasn't a huge part of the overall score.

still doesn't mean they should have it.

The game presented a story to them, should they just ignore it because it's bad?

What story? O_o it doesn't have one! , the minute you start the game this guy with a hat talks about the carnival and how much fun you are going to get by selecting gameplay modes in the menu and try to explain each gameplay type , thats not story!

Story isn't just something being explicitly told to you by an NPC, it's also the general atmosphere and context under which you play the game.  The fact that they made up a carnival for the gameplay setting means that there is a story even if it isn't specifically told to you by the guy with a hat.  If you don't think that is a story then you would have to not count Flower as having a story either, which would be an unfortunate oversimplification of what a story means.

When a game doesn't have a story they cut out that category, but when one is presented (even if it is just a pretense at the beginning of the game to get into the gameplay) I think it's legitimate to score on it.  And then how that score affects the overall would be based on how much they think the story for better or for worse affected the game as a whole.

edit: and if you look at the scores it was 5.5, 8.2 and 8.6 with an overall of 8.3 so it's obvious the story wasn't a huge part of the overall score.

So they score the story part based on if a story is presented to them, and they cut out the category if there is no story. And if the story is not a big part of the game, then it won't affect the final score that much? Seems fair to me.

If you look at the comment I replied to, the guy said that they used story as a sub category for all reviews, and that was what I was against.