IANAL, nor have I carefully followed this case. So I don't know what the jury considered or didn't consider.
It is my understanding, that there are several possible issues. First, did the convict help precipitate the confrontation? If so, then it might have been considered mutual combat. If the incident is considered mutual combat, then you may not be able to claim self defense, even if turns very bad.
Second, from my notes at LFI-1, in a one-on-one fight against an unarmed attacker, it is typically very difficult to legally justify lethal force. While you are correct that some people have died from fists and feet, the vast majority of fistfights do not result in death. Lethal force is only justified if you are in immediate danger of death or grave bodily injury. Fistfights rarely rise to that level of risk.
There are exceptions, of course. Force of numbers -- say 3 against 1. Vast disparity in force, e.g., large differences in size and/or age. Male against female. An aggressor who you know has unusual capability -- e.g., Chuck Lidell says he's going to kill you as he raises his fists and moves forward towards you.
But in a garden variety fist fight you'll have a hard time legally justifying deadly force.