Do you agree that there's more than 2 genders?

You did a nice job breaking out the genetic variations that make these waters a bit murky. But I do recall my biology professor telling us male and female are physiologically determined by the presence of either ovarian tissue or testicular tissue. Even in the case of hermaphrodites or intersex with vestigial genitalia of both genders, they typically will only present one of those tissue types...either ovarian only or testicular only, hence defining them as either male or female. In very rare cases, both tissue types have been present...then, I don't know. Flip a coin? I suppose you could try to make an argument for a 3rd gender.