You are on the right track. One concern I have, though, is that the prompt asks you who you think is "more" manipulative, implying that both of the characters are in fact trying to manipulate each other. You don't argue that. You argue that the man is manipulative and that the woman is not. This is difficult to sustain, even with the quotations you have picked. For instance:
"Then I'll do it. Because I don't care about me,
This is a classic form of manipulation via the guilt trip, with the comment meant to provoke the man into providing emotional reassurance and support.
Indeed, one of the most interesting aspects of the conversation is that the characters each want the other one to take ultimate responsibility for the decision. Jig can convince the man to "go through with it," but wants him to say they should
keep the baby. The man can convince Jig to terminate her pregnancy, but wants her to say she's okay with the decision to do so. This is psychologically realistic, as this is obviously a couple whose entire lifestyle is dedicated to having fun and avoiding responsibility as much as possible. It is perfectly fine to say that the man is the more manipulative of the two, but to argue that he alone is manipulative is a much more difficult task.