I think that the problem with them over in the states is that they don't really understand what they are singing about (not taking the piss here). A lot of it is about life in England (up north mainly) and i guess thats pretty hard for a lot of Americans to understand. That review did not really put up a good arguement to why they are crap, for example 'Arctic Monkeys sing about girls and drinking and being famous' is a stupid comment, as i can't think of song in which they do that. After all, they don't like the idea of being famous, and most of the songs were written when only a few people in Sheffield knew about them.
Maybe its because of the fact that the lyrics don't relate to your side of pond, and maybe that could limit their success over there until they get more widely accepted and have played some more gigs. All i know is that over here they've brought together a wide cross section of society who appreciate the music. When i saw them the last time they played in Sheff before the world tour, we had skaters singing with football hooligans stood next to 40 somethings. You don't see that very often.
Download some more songs (and translate some lyrics) and see what you think, i reckon you will like. Don't watch the SNL show though...apparently it wasn't too good.