"They are listening to that man."
Translation:Oni słuchają tamtego mężczyzny.
Well, prepositions generally work very differently for each pair of languages, it doesn't make much sense to learn their translations but rather to learn how they work with other words (so you learn that "iść do" means "to go to").
"słuchać" just takes a noun in Genitive, no preposition, you need to remember that the 'to' part isn't translated.
Incidentally, you may notice that "to hear" is a very similar verb but it doesn't take any preposition (neither in English and Polish), and there isn't exactly any logic to it, it just doesn't.
Yes, it's Genitive.
Oni słuchają tamtego mężczyzny. ("słuchać" + Genitive)
They are listening to that man.
Oni słyszą tamtego mężczyznę. ("słyszeć" + Accusative)
They hear that man.
Genitive - Dopełniacz, Accusative - Biernik (in Polish) https://pl.wiktionary.org/wiki/m%C4%99%C5%BCczyzna