I notice how you neglect to mention nor address his thesis. For the section you are citing, the author stated his position is: "On average, men and women biologically differ", and used the evidence you listed to back this up.

>Human universals

In your criticism, you are responding to an incorrect interpretation of this term.

When evolutionary biologists refer to this term, they are referencing the work of anthropologist Donald Brown, who compiled a list of traits shared among all known human cultures. He said traits on this list "comprise those features of culture, society, language, behavior, and psyche for which there are no known exception."

You can read a copy of this list here http://joelvelasco.net/teaching/2890/brownlisthumanuniversal.... Notice how this list supports his claim that "On average, men and women biologically differ".

>They often have clear biological causes and links to prenatal testosterone

A lot of the studies supporting this come from suffers of congenital adrenal hyperplasia (CAH).

Hines, M, Brook, C, & Conway, G. S. (2004). Androgen and psychosexual development: Core gender identity, sexual orientation, and recalled childhood gender role behavior in women and men with congenital adrenal hyperplasia (CAH). Journal of Sex Research, 41, 75-81.

Hines, M, Fane, B. A, Pasterski, V. L, Mathews, G. A, Conway, G. S, &. Brook, C. (2003). Spatial abilities following prenatal androgen abnormality: Targeting and mental rotations performance in individuals with congenital adrenal hyperplasia. Psychoneuroendocrinobgy, 28, 1010-1026.

Hines, M , Golombok, S , Rust, J , Johnston, K. J , & Golding, J. (2002). Testosterone during pregnancy and gender role behavior of preschool children: A longitudinal, population study. Child Development, 73, 1678-1687.

Hines, M , & Kaufman, F. R. (1994). Androgens and the development of human sex-typical behavior: Rough-and-tumble play and sex of preferred playmates in children with congenital adrenal hyperplasia (CAH). Child Devebpment, 65, 1042-1053.

>Biological males that were castrated at birth and raised as females often still identify and act like males

I think he's referring to the case of David Reimer https://en.wikipedia.org/wiki/David_Reimer . I don't believe we've done human castration studies, but we have done studies on mice that support this conclusion

Williams, C. L, Barnett, A. M, & Meek, W. H. (1990). Organizational effects of early gonadal secretions on sexual differentiation in spatial ability. Behavioral Neuroscience, 104, 84-97.

Williams, C. L, & Meek, W. H. (1991). The organizational effects of gonadal steroids on sexually dimorphic spatial ability. Psychoneuroendocrinobgy, 16, 155-176.

>The underlying traits are highly heritable

This one's pretty basic. They're heritable because many Sex differences caused by the existence of the Y-chromosome, which is heritable.

>They’re exactly what we would predict from an evolutionary psychology perspective

Evolutionary psychology is the result of analyzing ecological theories observed in other animals, and applying them to humans. Ecologists have observed differences between males and females in thousands of non-human species. Why would our own species be exempt? Even today, evolution itself is still considered very controversial https://en.wikipedia.org/wiki/Objections_to_evolution

So far, all his claims look all right to me. They support his claim that "On average, men and women biologically differ". And evolutionary psychologists agree on this one. http://quillette.com/2017/08/07/google-memo-four-scientists-...