The memo didn't claim anything about efficacy in engineering, period.

It claimed some contribution of biology to career preference on average, which is absolutely supported by research :

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3166361/

"We explored the contribution of sex hormones to career-related interests, in particular studying whether prenatal androgens affect interests through psychological orientation to Things versus People. We examined this question in individuals with congenital adrenal hyperplasia (CAH), who have atypical exposure to androgens early in development, and their unaffected siblings (total N = 125 aged 9 to 26 years). Females with CAH had more interest in Things versus People than did unaffected females, and variations among females with CAH reflected variations in their degree of androgen exposure. Results provide strong support for hormonal influences on interest in occupations characterized by working with Things versus People."

Don't you think that, considering trying to get women into STEM fields is a pretty recent effort, jumping to the conclusion that "it must be because of biological reasons" that they are not interested and then we "shouldn't be doing anything"?

Would you have held the same opinion, had I said "well, there might be biological evidence that African-Americans are not interested in going through higher education, so we should not worry about trying to help poor black kids go through university" 40 years ago?

It's still a giant leap to say that women are less likely to choose roles in tech and leadership, as Damore did.

It's fair to claim that as a theory, but in many places in his memo, he speaks as if it is established scientific fact.

I don't think the author specifically claimed that men are better at engineering (if he did, I'd love if you could point me to where).

I think he said that biological mental differences on average are one possible component of why engineers tend to be men.