Animals are motivated to kill their competitors. Any species that didn't become extinct as a direct result of a natural catastrophe was out-competed. That's genocide. The only difference is that when Humans act on that impulse, they can put their intellectual capacity and technology behind it. Again, it's acting on instinct rather than rationalism.
I'm not disputing that, but "competitors" are those creatures in their immediate vicinity, as JarodRussell pointed out when a lion takes over a pride it will kill the cubs of their defeated father. It doesn't then start seeking out all lion cubs to kill, nor conspire with other lions to wipe out other creatures because of some physical or cultural distinctiveness.
Yes, you could say genocide a form of "fear threat" response, to perceive a certain kind of people as a competitor or infringement on resources and wipe them out because of it, but this is a very deliberate and calculating kind of thing, something animals do not do. We have never observed elephants or dolphins doing it either, the more intelligent of the animal kingdom.