Do I think that a dog chasing down and attacking a cat predisposes it to attacking a human? Even a small human? No. Remember, there are many, many hunting dogs bred even to this day for this purpose. It was the original purpose of man using dogs. My DH owns several hunting dogs, and our kids are right there when they go hunting. (Not something I do, but DH's thing).
That being said, this dog did show aggression toward humans, it clearly was acting threatening toward the older lady, and I think I read toward another person in the neighborhood? So in this case, I agree that the dog needs to be put down.
Do I think all Pit Bulls are just like this one? No. But it is a breed that I have my guard up around at all times.