Street Fighting is not like your trying to kill someone. The goal is to knock your opponent out or make them tap out. Its essentially MMA without pads. And before you claim that its too dangerous and you need to have pads, consider American Football (Pads) and Rugby (No pads). It is incredibly organize, people get paid for winning fights, it draws in an audience, people will train for it, and they can even make a living out of it. It has every element of a sport. Nobody dies in Street Fighting, yet people have died in things like Football and Boxing.
We all know there is something called a "martial art", but not everything that is competetive is considered sport. In a sport, the objective is to do some kind of objective, not kill people. Sure the same may be said for pro wrestling, but at least there is an objective and that is to pin your opponent. So is not a sport. Even if is competitive. Is not a sport