He was an older guy, not slapping females was more relevant in his generation. (Also, looked like he just wanted to sit down and eat dinner and not start a fight.) I agree it’d be unacceptable for a modern dude to apologize after slapping a female who was initially violent towards him.
The guy would’ve let her walk if there wasn’t a bunch of people watching. But then again, she also punched him BECAUSE there was people watching and she wanted to look tough/brave/cool/whatever. Stupid chicks like this need to realize that chivalry is dead and they killed it. The days of the white knight rushing in to defend their honor are gone.