I don't believe that's why James Damore was fired. He was fired for a much more obvious reason: he was working against their efforts to have a more gender diverse workforce and he embarrassed the company in a very public way.
"First, let me say that we strongly support the right of Googlers to express themselves, and much of what was in that memo is fair to debate, regardless of whether a vast majority of Googlers disagree with it."[0]
Google admits that there are some things in the memo that are debatable, even though Google disagrees with Damore.
"It is contrary to our basic values and our Code of Conduct, which expects ‘each Googler to do their utmost to create a workplace culture that is free of harassment, intimidation, bias and unlawful discrimination"[0]
And that is why he was fired: deliberately working against Google's workplace culture goals. There may be room to argue about what Damore may have meant, in his heart, when he wrote the memo. However, since the memo is a physical artifact that we may all inspect, it's clear that the text of the memo is unabashedly sexist. He clearly states that he believes the gender gap at Google is not caused by sexism and that's at clear odds with Google's goals.
"We need to stop assuming that gender gaps imply sexism."[1]
As if it needs to be said, that is clearly not the case. The primary cause of the gender gap is very much sexism and it's a real problem that needs to be dealt with. While we may disagree on which steps will be most effective, there's no benefit to denying the problem exists.
[0]: https://techcrunch.com/2017/08/07/google-fires-memo-author/
[1]: https://medium.com/@Cernovich/full-james-damore-memo-uncenso...