> Why should a human have a moral responsibility towards non-humans, while a cat doesn't have a moral responsibility towards non-cats, just because the human is capable of making moral judgements?

Because as a human you recognize patterns in other animals that are similar to ours - the deepest pattern being alive - so you can project your feelings over them. This is also called empathy, and some in our kind lack it completely, but I would dare to say that is globally one of the defining traits of the human species.