No, it doesn't. Gender (which is distinct from both sex and gender identity, though there is an increasingly popular modern view that gender should be ascribed based on gender identity) is a socially ascribed trait, and different societies have recognized different numbers of genders and used different methods of ascribing them.
> The vast majority of cases you see today with people claiming to be the sex they're not are psychological, not physical.
The idea that there is such a thing as “psychological, not physical” is mystical woo that has no place in fact-based discussion, and divergences between gender identity and gender ascribed based on sex determined by chromosome counting has an observed correlation with other physical divergences from typical traits for the assigned sex.