No he didn't. Why is this lie still being spread?
He started from the point of view that the current state is optimal in terms of outcomes for Google and then sought to construct reasons justifying it - the principle reason being that women were not genetically predisposed to hack it in the hot house of male competitiveness.
What he did not do is offer any evidence that the current state was optimal, he just took it for granted that he could not be part of a suboptimal system. He offered no evidence that the outcomes for Google were better or worse as a result of their diversity policies, he just assumed that the candidates being hired under that policy were inherently inferior.
He said I don’t think we should do arbitrary social engineering of tech just to make it appealing to equal portions of both men and women. - an unqualified statement that makes no reference to whether such a change would have better or worse outcomes for Google, he simply assumes that the result will be worse.
Indeed, it's not clear that he understands what outcomes actually count. He says those willing to work extra hours or take extra stress will inevitably get ahead - by which he means mostly men. Yet that pretty much defines the kind of employee you don't want: the stressed low-productivity presentee.
Now, I suspect that Google is sufficiently chaotic in its hiring and its management that it doesn't have any useful metric for outcomes - they produce too much that they throw away. And if Google don't have those statistics, Damore has none.That leaves the value of their former hiring policy as moot as their more recent policy and Damore's belief in the inevitability of gender imabalance is simply post hoc ergo propter hoc.
It's hard to view an argument based on no evidence that is basically "engineering has always been done this way by tough men and touchy-feely women are repelled by it" as anything other than "women's brains are just not inherently suited to engineering jobs" if you're also asserting those jobs cannot be done differently.