Well, I don't know about US law at all, but the first video was from the UK, the second from South Africa, so US law is really no more relevant than any other jurisdiction. UK law states that the person who made the first aggressive action cannot rely on self-defence, even if they are not acting with violence in the immediate lead-up to the incident. In the first video it's difficult to see who started the incident as we join it while hostilities are already under way. The same with the second video, but in that case we are told that the man who hit the girl initiated the violence.
I'd say that in the case of the first video the man in green could make a defence, but I'd want to see the entire tape to see who started the whole situation.
In the case of the second, and if there are witnesses to testify to who threw the first punch, I'd say the guy is bang to rights. I'm a bit surprised that you seem willing to exonerate such violent behaviour so quickly.
In the first video, the first person to initiate actual violence is the woman. If the man in green were acting in a threatening manner prior, it is not readily evident, but information is limited. I'm going by the vid, as that is all I have on hand.
In the second vid, two men were fighting. Who started it, I cannot say as the video does not show it. The women interposes her body and punches the man in the face; that is the first act of violence between them as far as the video shows. He punches her back immediately, while she was still lingering in range aggressively.
I know very little about UK or SA law on such matters; I can only comment from the framework of my own legal system.
Again: I don't know what happened prior to the vids, I don't know what was said, and these things could be relevant.
However, going by just what I SEE, I see two cases where a woman initiated violence against a man, and where the men REACTED to the violence with force that could easily be construed as self-defense based on available information.
Stepping away from questions of strict legality, let's address the moral or ethical circumstances: In both cases, Person A struck Person B first. Absent some good reason I cannot determine from the vids, this is assault. In my own ethical/moral framework, one is allowed to use violence when assaulted with violence. Any other view simply makes good persons into easy and attractive victims.
Or to put it more succinctly: Don't wanna get hit back? Don't throw the first blow.