Is this a horror movie? It's definitely a monster movie, but by being a monster movie is it automatically a horror film? I think that it isn't. But that's just my opinion.
Monsters got a lot of publicity from the fact that Gareth Edwards did most of it on his own, and with almost no budget. He did a great job making what looks like a big budget Hollywood film on the cheap, with quite a bit of CG that looks pretty decent. He also goes the Hollywood route by having a barely there story and characters who don't really say or do all that much.
It was good enough to get him a gig directing the big budget Godzilla movie. I didn't dislike it, but, I felt it didn't really do much, and wasn't a horror film.