The people that need to "win" drive me crazy. It's not enough to them if you concede on some points, it's not enough if you agree to disagree, they just have to be right 100%, and you realize they won't be happy unless you say "Sorry, I was wrong and you were right." and bow to their superior intelligence.
I've made the mistake of engaging with people like this before and it was a nightmare. Like you said, they wouldn't just drop it, even after I explicitly said "Sorry, but we are going in circles here, we should just end it." after an hour long discussion, where they could've easily taken their "W" from me walking away.