All the rugby enthusiasts could join up together as a group to camp together, but not necessarily as a registered theme camp. There isn't much commitment to doing that, other than hanging with people that have like interests and sharing your resources and chores. If you are all traveling from overseas, you would only need one camping stove for the whole group as an example of sharing. One person may be a really good cook, and others may be great at pounding stakes and setting up tents and shade.
Burning Man is traditionally not a sporting type of event, but I have seen giant croquet, bowling, golf etc. out on the open playa. The thing to keep in mind is to keep it really creative, fun, don't expect to ever keep a real score of the game. A thought might be to move the game after every 2 goals, by using orange traffic cones. This would allow an instant game to pop up near a crowd, then disappear as quickly as it showed up. Clothing is optional.
The main thing is to keep it creative and fun.