Are Gladiators Playing a Game?

Today some students in my games course asked me if I could provide an alternative question for their current assignment. this puzzled me, as I thought "Analyse reactions to games in terms of moral panic" and "Can actions in a virtual world have moral significance?" were both easy and fun, but I promised to try and think of one. While they were studying a fiendishly difficult text about the infamous lambdaMOO cyber-rape, full of words like "illocutionary" and "perlocutionary", I pondered and came up with the question: Are gladiators playing a game?

This popped into my head as a result of a comment I made about seriousness not precluding something being a game: "Think of the last scene in Gladiator where Maximus' soul is wafting away after he's been killed by Commodus. He probably wasn't thinking 'Oh well, it's only a game.'" Gladiatorial combat was in some sense a game; in fact, we speak of "gladiatorial games". But were the gladiators themselves playing a game?