Like I have said many times, I think that US police are out of control these days.... but having said that, there is the following in this case:
First of all, off duty or not, a sworn peace officer is still a sworn peace officer, even if he happens to be standing around eating a hot dog, or whatever.
Secondly, if there was an physical altercation with the fire fighter and the cab driver, then as a sworn peace officer, it is his right, and duty to get involved.
Thirdly, if he steps in, and identifies himself, and one of the people fighting takes off and runs, then he has every right to chase that person down. He has no idea why they are running, maybe they just committed a murder, he doesn't know, and he has the right to detain that person in order to find out.
Fourthly, when he catches up to him, and then tries to restrain him with handcuffs, and the suspect overpowers him and starts hitting him in the head when he is down, this is a VERY dangerous situation for the officer. If the guy succeeds in knocking him out, there is no stopping him from taking the officer's weapon and using it on the officer and other people. At that point, the officer had a right to use deadly force to stop the suspect.
AGAIN, I think that the police these days are more about protecting themselves rather than the community, and the shooting of people, their dogs, etc... the serving of no-knock SWAT type warrants for everything under the sun, etc... the amount of military equipment being issued to local police, etc... are all things that are really bad and out of control.... But in this instance, the guy was beating on a police officer who was all alone, and I would have done the same thing in the officers place.
.
.