I believe it would be simple assault unless the victim was hurt in some manner. My Father was a high school teacher for about 25 years, and once he and another teacher had to restrain a student. He took a swing at me father but since he didn't hurt him, the student was charged with simple assault.
Of course he wasn't a member of a protected class like code pink is, so getting him charged and convicted was a simple matter. Doing the same to that scurvy bunch Code Pink, next to impossible.
It may differ among the states, but IIRC, "Assault" can be anything that conceivably constitutes the presentation of a threat; a sudden change in posture, taking a swing, flashing a weapon, whatever. "Battery" is when physical contact is made in the course of an assault.
There's enough on the video to support filing criminal charges. Others present could be deposed.
Keep those cameras rolling and get one back in the ranks to capture what happens to the videographer out front.