The gross oversimplified claims from the document that attempt to make this leap are textbook stereotypes.
For the n million-th time : the memo said nothing about aptitude for engineering, just preference.
Nonetheless, many of the statements in "Personality differences", "Men's higher drive for status", and "Non-discriminatory ways to reduce the gender gap", especially the stuff about women being more prone to anxiety, liking part-time work, caring more about people than things, etc. speak strongly to aptitude for engineering, given the context of the document.
EDIT: Also, I reject the implication that the claim "women have less of a preference for engineering" is not in and of itself a harmful stereotype.
1. The memo uses the word "preference" without ever establishing whether it's talking about free choice or choice after discouragement, and so is flagrantly begging the question.
2. It's simply false that the memo makes no connection between supposed preference and aptitude, as it builds to a section about the "harms of diversity" that includes a direct claim that women in Google's workforce are less capable than men.
I have been confused why you and others have been repeating this, but after re-reading the section "The Harm of Google’s biases", I think I see your point now.
Damore does not say that all women who work at Google are unqualified, but he does imply that there are fewer women who are qualified, and that by trying to mine that population too heavily, Google is hiring women who are, on average, less qualified than the men are, on average. Do I have that right?
Of course it's talking about free choice. Introducing "discouragement" in the equation is itself begging the question : it's an extra hypothesis which is unnecessary in presence of a simpler, more fundamental explanation (like this one https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3166361/ ). Occam's Razor 101.
> includes a direct claim that women in Google's workforce are less capable than men.
Citation needed.