Generally speaking, when someone is choosing to spend their first date with you talking about another man who is pursuing her and who she is interested in—well, I'd say that's the moment to fold up the tent and search for better soil.
In other words, this has nothing to do with you, what you did or didn't do, and everything to do with her being into him. Perhaps she thought and/or hoped, as humans often do, that meeting a new person would zap this dude out of her system. Or perhaps she...really, it's not worth examining.
Most people we go on dates with will go nowhere. That's just the fact of it: part of the fun, part of the agony. Dust off and keep doing what you're doing.
bluecastle's post in Was this second guy a red flag from the start? was marked as the answer