Why does he call sex "gender"?
The word "sex" is derived from a root meaning "cut", from which we also get "sector", "secant" and probably a few other words. We cut the species into two sections or sexes, which are persistent conjugal strains; we can imagine that on some other world there might be a sectioning into more than 2 sexes.
The word "gender" is derived from a root meaning "kind" or "race", also a kind of division; from the same root we get "genus". The word's principal proper use is in grammar, as a natural mapping of a noun to words or particles meaning he/she/it or the like. In English we have 3 genders, in Spanish 2. Because the English and Spanish genders have some parallelism to sex of the object the noun refers to, we call the genders in such languages by names paralleling the names for the sexes, but that need not be: in Swahili there are 8 genders, with no parallelism to sex; in SeSotho, I am told, there are 6; many African (technically, Niger-Kordofanian) and Australian languages have such sex-independent gender systems.
Let us call sex "sex" and not be embarrassed about it.