Haha, I love this question!
In my mind, I've been imagining this whole game as a forum adaptation of a typical video game beat'em up. These two characters are selected by some omnipotent being (traditionally 'you, the player' but in this case, me and a randomizer app) and put into some random place against another. They didn't choose to live under these circumstances. All they know is, to get out of them, if only for a time, they have to knock the other opponent out. It's all they know. It's all a bit tragic really!!!!
But it's funny that the idea of fighting has been brought up because, though I have clearly stated these characters are involved in 'fights', I wonder if all of them need to be won by strength, ya know? I've wondered if anyone was gonna try to argue that one character would taunt the other in submission after giving some convincing backstory as to why the losing champion has such little confidence or why a specific taunt would work. Or mayhaps one champ would seduce the other! Could Cloud's mum have won had she lulled the Time Guardian into a false sense of security by showing it the kind of affections that is had never known? Like, 'Wow, Mrs Strife! You know, in all these centuries, you're the first one to ask me how my day has gone and whether or not I'm hungry. Oh, and you're the first to care enough to scold me for stinking up the place having gone a near millenia without showering. Is...is that a pot roast you're preparing for me? I'm not even sure if I have the organs to digest this but.... *does the magic time rock equivalent of crying*... thank you. "
WHO KNOWS!
It's gonna be interesting to see how the rest of the rounds turn out though, hahaha.