It's certainly not jump scare horror; it's more existential.

I enjoy horror movies, but they've long since stopped "scaring" me. To me, they're mostly just fun -- seeing the effects, the ways they'll put their own twists on genre tropes, etc.

Annihilation, for me, invoked a true sense of dread and, well, horror. It's several years old but still lingers with me.

(After writing this I realized you said 2013, not 2018... hope that's just a typo and we're talking about the same movie)

I would call it existential horror. It has a threat that is beyond understanding and a faith possibly worse than death for some characters.

Apart from that it has great themes. A fantastic movie overall

I would say so. It's kind of a non-central example of the genre but I think there's enough horror there.

I'm terrible at horror movies. The bear was in my mind for months. Even now it still comes to mind when I'm closing my eyes in the shower.

I did not read the billing, did not realize it was at all a horror movie going in.

I think my criteria for if something's a horror movie is answering this question: is it trying to scare me, or otherwise make me uncomfortable? If yes, then I think it belongs in the category to some degree. A lot of angst is spent by genre fans (horror especially, I've noticed?) wondering if something belongs in the genre, and I personally think a lot of it is unnecessary.

Enjoy what you enjoy, and if it spooks ya then I think it's fair to at least say it has horror elements.

I wouldn't. Some creepy moments (that bear that screams!), but never scary.