I don't understand why asking for a favorite football team is a "gender based question". Women clearly watch football, and TBH, calling that a gender based question is more demeaning to women than the actual question.
That said, I don't think that particular question is sexist. Football (particularly in the midwest where Mayer hails from), is pretty broadly popular across gender lines to the point where it's not uncommon enough for women to like football that it would be effective in exclusion signaling.
Sometimes questions like that are an attempt at signaling exclusion. The purpose is to remind you that you're different from the group. It's really irrelevant to the quality of the question whether you were actually the school's star track athlete, or instead spent all your time hacking on your computer. It's even irrelevant whether the stereotype is actually true (I don't know if people at tech startups are less likely to have played sports in college than people at investment banks). All that needs to exist is a clear stereotype and for both sides to be aware of the appeal to that stereotype.