There will be animals in the game, not sure about fighting or hunting. I'm sure in some wilderness/outdoorsy areas you may be able to shoot rabbits, birds, deer, but I doubt there'll be a dedicated hunting system with skinning and the like. But you may be able to loot them, like in TW3.
As HK said, cats are confirmed, I believe Vattier (CDPR PR guy, I think) also said other animals will be in, potentially dogs and the like.
In other words, this world isn't Blade Runner. Organic life (outside of humans) isn't completely obsolete and extinct, and I doubt most people are going to bother augmenting their pets unless it's to keep track of them or for medical purposes (give a cat with arthritis metal limbs). When you think about the number of stray animals, think closer to our world than other Cyberpunk universes.
People love (or love to hate) dogs and cats, and that probably isn't going to change just because it's the future. Barring extreme situations, people in western civilizations generally don't hunt pets, so I doubt their numbers will dwindle for no reason. Now, exotic animals? That's another story.
