We don't have to guess because while a final NLRB ruling on the topic was not given (due to Damore withdrawing his labor complaint for unlawful termination), the published memorandum from Jayme Sophir regarding the case suggests strongly that judges would have ruled Damore's speech unprotected and, therefore, the termination legal.

https://www.nlrb.gov/case/32-CA-205351

""" [] statements about immutable traits linked to sex—such as women’s heightened neuroticism and men’s prevalence at the top of the IQ distribution—were discriminatory and constituted sexual harassment, notwithstanding [] effort to cloak [] comments with “scientific” references and analysis, and notwithstanding “not all women” disclaimers... Once the memorandum was shared publicly, at least two female engineering candidates withdrew from consideration and explicitly named the memo as their reason for doing so. Thus, while much of the Charging Party’s memorandum was likely protected, the statements regarding biological differences between the sexes were so harmful, discriminatory, and disruptive as to be unprotected. """