Earlier quoted context omitted.
Is there a name for this rhetorical form? If X was a true Y, they would do what I say all Ys should do.
Yeah, the "No True Scotsman" fallacy: https://en.wikipedia.org/wiki/No_true_Scotsman
Is it not true that a supporter of freedom of speech would support other people's freedom to disagree with him without being doxxed by his supporters?
It seems to me that it is true, at least if the supporter's conception of freedom of speech includes freedom from harassment after speaking, which Damore certainly appears to be believe to be true.
Having said that, although I think it would be commendable for him to publically rebuke doxxers, it is fallacious to argue that his support for freedom of speech carries with it an obligation to do so.