While that’s a good idea, I’m not convinced your conclusion is correct. But maybe I’m just missing something. Why would they eventually arrive at a win, and not a draw?

Yes, that would let you know if the one you asked tells the truth or lies. But IIRC those riddles are usually constructed such that that is not enough to solve them. For example, sometimes there are more than two people that you need to identify. Or you need to find the correct door amongst multiple. All with a single question to one of the people.