This is no exception, but it has nothing to do with her being a woman. The video is incomplete, but I can see no possible reason for a cop to punch in the face a prone person. They need to facilitate arrest by controlling her wrists and tackling if need be. They were doing a poor job of that, too. I agree the video does not show the inciting incident that made the police angry. That makes his reaction a lot more understandable. But not appropriate. I really doubt firing him is just punishment, although I'd like to know more about how different his behavior is than those on his unit to compare.
See I just don't think it is relevant what she may have done to make him angry. Cops are supposed to be trained and are definitely paid to remain in control. Punching her in the temple and face while she was on the ground with two men on top of her did absolutely nothing to help the situation. "She made me angry" has never been an excuse to punch a woman like that, cop or not.
In my opinion the really scary thing is how willing they are to do shit like this with a fuckton of witnesses all around them. Just imagine what that cop might do if someone makes him angry and there is no one around.