An animal only does something if it is to his or her advantage. So what advantage is there in having two cats fight over territory? I can think of only one right now having just seen the video.
Cats attack birds as a prey item, as food. If there are two cats in one area the crow has two predators to deal with. If they fight each other, one cat wins and the other leaves the territory leaving one predator for the crow. The crow has an easier life on the assumption that he stays in the area which might be the case as he probably has a source of food there.
Crows are very smart animals and I would have thought that that sort of reasoning is within his or her capabilities.