As with any issue worth talking about, Damore's memo isn't outright sexist or discriminatory--but it isn't the well reasoned call to arms for an individualistic approach to diversity or a reconsideration of biology that he might've hoped for it to be.
Some of Damore's footnotes reveal he lacks a certain subtly and researcher's tact and has quite a hefty number of biases of his own:
"Communism promised to be both morally and economically superior to capitalism, but every attempt
became morally corrupt and an economic failure. As it became clear that the working class of the liberal
democracies wasn’t going to overthrow their “capitalist oppressors,” the Marxist intellectuals transitioned
from class warfare to gender and race politics. The core oppressor-oppressed dynamics remained, but
now the oppressor is the “white, straight, cis-gendered patriarchy.” -- Damore, note 7.
This is a polluted conceptualization of the issue and outright mythology. You can tell from his phrasing he's fallen prey to the us v. them mentality that plagues many of those who rail against the 'sjws'--linking identity politics directly to marxism and its development is patently ridiculous, a bleeding of domains, and shows that he can't help letting his own biases color his reading of contemporary situations and narratives. Sure, there are offshoots and links between these struggles but--I mean seriously--does he really believe there's some cohort of marxists who collectively decided, 'man we got to overthrow capitalism somehow but the proletariat didn't do it so lets try to level gender and race inequalities' what? Are we in fairytale land? There are people who research and write about identity politics that may draw upon marxist thought in some of their critiques, but it isn't some legion of people who just want to consistently uphold an 'opressor-opressed' dynamic regardless of the participants. There are plenty of marxists who also find identity politics to be total hogwash. For a memo that tries to "advocat[e] for quite the opposite: treat people as individuals, not as just another member of their group (tribalism).", it fails spectacularly at its mission in this footnote.
Damore's document is not a sexist screed by any means, but it isn't some lucid reconsideration of diversity either--plenty of his word choices and preemptive defensive measures (see the several instances where he reiterates that he definitely not a sexist and definitely supports diversity) show that, even if he was making an honest effort to step back, he is still victim to particular ideologies.
We should ask ourselves why Damore would write such an memo in the first place. He makes no direct mention of an incident that prompted this call to arms. No quantitative predictive analysis into how a change in Google's diversity program would improve it and foster greater diversity and make it 'psychologically safe'. This makes one think his primary motivation was more likely a personal sense of injustice, or fueled by adherence to an ideology (his conservatism). It sounds like the result of a personal incident in which Damore's ideas were challenged, and he felt the instance was the result of company wide systemic practices and not an individual issue.
I can't say whether or not the firing was justified, but Damore definitely isn't the scientific, neutral paragon Brooks reads him to be. The memo is loaded with ideology. It is not a scientific paper--nor does it claim to be. It is a political argument that tries to mask how politicized it is under the protective badge of 'but I have science on my side'. There's some ridiculous idea that, so long as science is on your team you're in the right. People forget that science only describes the world. What we argue for using science and how we interpret it still point inevitably to our own values. Just because you can leverage scientific fact to push your agenda does not make it 'correct' or 'objective'. Yes, science tells us the world is getting really hot and we should probably stop that if we want to avoid major climactic shifts--but science doesn't tell us we should act to save the world--that's up to us. Hell, the universe might be better off if the world does go to ash. There's no way to know. you make a value judgement and you act, scientific or otherwise. Even Damore's urging that we de-moralize, and de-empathize and generally act more like inhuman robots when it comes to diversity to depoliticize it is a major value judgement (that it's valuable to be neutral and objective and science guided as possible) and is thus both moral and political.