Private companies are not free speech zones. Not firing this person would have been a Title VII violation and opened them to lawsuits.
I disagree. His manifesto is pretty clearly core political speech protected by the First Amendment, so Title VII would be unconstitutional as applied if it operates to force Google to suppress such speech. Unfortunately there is no precedent clearly establishing this, so the mere threat of lawsuits (and accompanying legal expenses) may have been a factor in Google deciding to fire him.