I guess that clears up the English translation... seems a bit obscure. As for the Arabic, I've never heard any of my Arab friends or Arabic speakers in general refer to a cat as a queen. The closest I can think of is that my Egyptian friend, Hesham, named his cat Iziz after the ancient Egyptian goddess.
Whether in English a female cat is called a queen (I, a native English speaker, didn't know that) it doesn't explain why in another exercise a grandmother is called a queen. I had asked whether calling a female being a queen was an accepted compliment in Arabic, but have received no reply. In English, it would be a compliment, but a rather extravagant one.