well. it is genitive because słuchać is one of the verbs that need genitive. On the other hand you can't tell with "cat" as it has accusative=genitive.
I'm assuming jazz terminology doesn't translate into Polish and this is a literal cat, but nonetheless I am holding out hope
"We are listening that cat" or "to" is needed in between and my English is that bad.
słuchać can mean either listen or hear. I should not get marked wrong for using listen in the translations. The source of the meaning is the book 301 Polish Verbs
You should not get marked wrong, because 'listen' means 'słuchać' and is exactly the right answer. It seems that sometimes there's a bug causing a correct answer to be rejected.
But I'd never say that 'słuchać' can mean both. Just like in English, we have separate words. If the book really says so... then I'm afraid the book is wrong :/
"to hear" is "słyszeć". "My słyszymy tamtego kota" would be "We hear that cat".