It's all about black humor (humour for you on the other side). Either amazingly painful things that have bad jokes made about them tickle you or they don't.
As a newspaper reporter, I discovered that any majorly awful disaster ended up with some really bad jokes told about it. I don't think it's shadenfreud, more like laughing in the face of pain and death.
Example (You are warned). Christa McAuliff's last words to her family (before leaving on her fatal trip as the first female astronaut) "You feed the dog and cat; I'll feed the fish". Like that.

Given that, I would be pretty sure Eric Bogle cares about cats, is fond of them.
And no one has mentioned yet that part of what is funny about "Nobody's Moggy Now" is that -- at least on his album -- Eric Bogle and friends render this as a perfect barbershop quartet Adding that touch -- a musical form that is rife with treacly gooey sentiment about the beauties of life and love -- just ices the cake for me.

It is the kind of song I enjoy thoroughly and don't want to hear very often.

Blessings,
Barbara