Competitions of mixed martial arts have been known to have existed since the Greco-Roman era. Modern MMA was begun in the 1920's with Brazil's Vale Tudo (Anything Goes) sport.
I don't really understand what you are asking. Is it a sport? Of course. To me athleticism is the physical conditioning/endurance/strength part. So under that generalization mma is very atheletic.
There are 5 dimensions in the MMA style itself. Wrestling, Kickboxing, Boxing, Muy Thai, and Brazilian Ju-Jitsu. All are used in many ways in the sport itself, there are many more styles used to make...