Real? He was breaking DC law and federal.
Fake? (1) Most jurisdictions treat facsimile guns as real, since the presentation of a realistic fake gun can be used as effectively as a real one -- armed robbery, muggings, terroristic threatening ... and, (2) if fake, that's a really stupid move. Brandishing a realistic-looking gun at a protest could get you shot by the cops OR another protestor who is really armed.
So, trying to factor in "real vs. fake" in this case really doesn't make much difference, if any.