I think it would be fairer to say that Gladiator is fiction, albeit based on historical data however distorted, but note also it is very similar in concept to Fall Of The Roman Empire but told from a different reference point.
In reality Commodus didn't kill his father to become Caesar - he was co-emperor for four years before Marcus Aurelius died. And of course Commodus wasn't killed in a gladiatorial contest. Having found a list of names that the listed assumed was their death sentence, a conspiracy was arranged for Commodus to die. An athlete was sent in to Commodus' bath where the infamous caesar was strangled.