You can be an unpleasant person and kind of an ass without being abusive though. While I don't like the guy, we haven't really been shown systematic, repeated emotional abuse... just that he is kind of a douche. Abusive? I think that's hyperbole - I mean I wouldn't want to hang out with him, nor date him, he is a shitty person. Abusive implies hurting another person, perhaps intentionally, perhaps not, to a degree far beyond what we've been shown.
And yeah, it's immensely shitty to beg for unprotected sex, whether straight sex, lesbian or... whatever sex. It's not abusive though, she could have told him to grow up and wear a rubber. Nothing in the situation implied to me she was trapped in it, felt forced or anything, it was just her own issues making her an idiot. A very human, sympathetic and infuriating idiot.
Love the story though, the guy is definitely an ass and if he isn't cheating he is going to soon.