Bisexual does not refer to gender, nor does it reinforce a gender binary.
No, it doesn’t. This idea has its roots in the anti-science, anti-Enlightenment philosophy that has ironically found a home within many Queer Studies departments at universities across the Anglophone world. While it is true that our society’s language and terminology do not necessarily reflect the full spectrum of human gender diversity, that is hardly the fault of people who are bi.
As a scientific term to describe sexuality, the word bisexual came into use during the late 19th century as a means of classifying people with both homosexual and heterosexual patterns of sexual attraction or sexual activity. The Latin prefix bi- does indeed indicate two or both. However, the “both” indicated in the word bisexual are merely homosexual (lit. same-sex) and heterosexual (lit. different sex).
Sexual orientation terms are grounded in biological sex, since it’s a more concrete and scientific concept than the more socially constructed, subjective, and malleable gender. To say that a person is bisexual is simply to say they are attracted to both the female and male sexes. Whatever gender-based attractions a bi person may or may not have fall outside of the parameter of the concept of bisexuality. Bisexuality does not reinforce a false gender binary because it does not pertain to gender at all.