Adam and the family had the custom of treating Alex like garbage in order to cut any kind of feeling or bond between them, this would make easier the

SPOILER
sacrifice of Alex

You can see howthe parents always scold Alex and let Josh go although the both of them are in the same problem...

When I first played I assumed it was a deer because of the photo you find of that room. But I'm starting to think it was the dog too, because it is missing and there are the ferals which look skinned. But it doesn't make sense since Alex asks where the dog is later. Wouldn't he have thought that way before when it was first killed?
Anyways I agree with the otherworld making the hunting room scary because of how Alex remembered it.

Yea. I always figured it was just a deer or other non-story related animal.