At the end of the day, I would always blame the woman and not the other dude if the woman you're talking to becomes more interested in him over you.
It doesn't matter if it's a woman you just started talking to, your girlfriend, or even your wife. If she starts showing signs of interest towards another guy instead of you, that's on her. Of course if she WAS your girlfriend or wife instead of some woman you just met and she does that, then you have a whole different problem on your hands.
But if the woman tells the man she's not interested and he keeps harassing her no matter what your relation is with her, that's a different story. Then it is on him and then it's time for you to step in especially if you're more serious with the woman.