"놀아 달라는 거자나" == "놀아 달라는 것이잖아." --> "You mean you want me to play(have time) with you(, don't you)?"

I'm asking you to hang out with me. It can be used in this situation - When he or she have tried to say that hang out with me in an indirect way, you didn't mention anything or you seemed like you didn't get the point.