Back in the day when a gladiator or some other kind of team won did they go back and destroy stuff? Or is this a new thing?

There was sometimes disorder between supporters of different gladiators, such as when Pompeii was banned from having gladiator games for ten years due to a riot between locals and people from the countryside. More often, though, riots happened due to the chariot races, which were more team-oriented - and even then, the riots were more common in Constantinople than in Rome, which was, by the time of the Empire, heavily garrisoned with paramilitary forces.