Chariot races were more popular than Gladiator games in ancient Roman world. There is a ancient TSR boardgame that seems to be fun.
Here some useful links:
https://www.boardgamegeek.com/boardgame/244/circus-maximus
https://www.boardgamegeek.com/boardgame/843/circus-minimus
https://ravenscraftcybernetics.com/circusmaximus/
Here another game with similar intentions:
https://www.boardgamegeek.com/boardgame/2224/circus-imperium