The video say so much and so little, all at the same time.
Does the male strike the female without provocation, or is he defending himself from her advancing upon him and trying to strike him in the chest?
Is the woman advancing upon the man and attempting to hit him in the chest, or she moving forward and raising her hands in a defensive stance to hold off an angry man who is charging her?
Did each mistakenly perceive the other was attacking them and engage in what they both thought was self defense?
Such a distinction is impossible to make from the video and best left for the halls of debate rather than a criminal court. Given that representatives from these two groups routinely come together at Berkeley to voluntarily engage each other in violence, most prosecutors often view such matters as "mutual combat," where both participants are criminally liable under Section 415 of the Penal Code, as cdwjava pointed out. Such cases are rarely prosecuted because they are just that - mutual combat.
It is naive to believe that the police would stop and take a time out in the middle of a riot to do a battery investigation, take names, addresses, interview victims & witnesses, find out the perception and intent of each participant to determine if this was an intentional battery or self defense, and write an investigation report while hundreds of people are tearing up the campus and downtown area. The police are going to be too busy trying to separate and disperse people, keeping the peace and arresting those who commit more serious crimes.
This is a "go nowhere crime" with respect to prosecuting either participant for striking the other. Civil court is the best venue if either party wishes to pursue it.

