The literal meaning of “emasculated” is castrated, although that’s no longer a polite way to refer to someone. Figuratively, you’re right: it means that a man has lost his male role, or been disempowered.
What is or isn’t sexist in what context is a complicated question, but I’d avoid calling someone else “emasculated“emasculated” or “emasculating.” It would be taken as an insult. The examples you give of polite usage are variations on, “He himself felt less masculine, but he shouldn’t have worried.”