Btw, in case I wasn't fully clear, I'm asking about the storyline of the entire RHG tournament itself, not the backstory we need to make for our RHG characters.
I think there is actually no permanent backstory behind RHG tournament itself. Well, probably stone's the one who invented it (not sure if there's others too aside of him), but then he left the creativity to us. It's really easy to manipulate and there are lots, lots of diversity of the story according to each animator/story thinker. Like...this might be the reason it's called "RHG Universe" because it's such a humongous "galaxy" and all.
If you think about RHG as a "headquarters" then go for it. Develop them by yourself. Hence, the creativity can work on that area, too.
Although yeah, basically, RHG Tourney's a match between two or more gladiators (I remember there was a 3-way RHG battles back then but it might be hard to make such commitment to battle your two opponents) in whatever condition. Be it inside a Colosseum type of arena, be it at the top of mountain, the setting can be whatever you want. In my version, RHG battle can be done on whatever setting and their fights are monitored overtime. There might be RHG leaders or something (e.g. FLLFFL, Yoyo, Andre, etc etc) and as a gladiator wins, they might get their rewards, sort of thing. I can explain it more but, probably I'd rather making a book out of it XD