Maybe there was a "sport" predating the invasion where humans were hunted (tormented cat-and-mouse style, or bullfighting style), which started as simply chasing down prey or eliminating pests and became a highly competitive sport with points for style, speed, hits, etc. Either they became more "civilized" and replaced it with an animal or inanimate object or they were forced to change it during the occupation, so the sport has become more symbolic than outright violent... but between themselves they know exactly what the "ball" or "target" really represents. (Maybe look at some of the nonlethal variants of bullfighting, which are about acrobatics or snatching a rosette or something from the animal, as a way a bloodsport could transform into something less bloody.)
Do be aware that, unless this has a direct bearing on the characters or story, working out all the intricacies and details of an entirely fictional sport can very easily become procrastination and another way to put off actually writing the story itself... It's also something where maybe details can be hammered out in second or third (or more) drafts, with just some vague allusions to "sport" and "goal" and "players" and such made as space-fillers in the first draft.
Though for a book that gets deep in the weeds of a fictional dragon-involved sport, you might take a look at Blazewrath Games by Amporo Oritz, though the dragons in it are companions of humans (for the most part...).
