He then responds, yes, that's true. But, if we ARE doing another round, plenty of others were disqualified under conditions they may consider unfair, either because the format switched to Battle Royal, or because Alicio, who was not a valid entrant, smashed up the ring.

I'm moslty just reading this as Lawful Oneupmanship. White Chain called him out on strict adherence to the rules, and he one-upped her by saying "Well, TECHNICALLY, a bunch of these people were not eliminated fairly according to the rules they entered by. So..."
Hmm.. no i think it seems pretty clear the one it might be unfair towards is White Chain.
He is talking about the warrior who won the bid when saying it might be unjust.

And how would it even work as Lawful Oneupmanship? This bonus round is only an advantage to White Chain.
As the few people smart enough not to take a swing.

This is more SD trying to be sporting. He is being challenged to a fight by someone already partially crippled from the previous rounds.
So he tries to make things a little more fair by entering into a fresh battle royale himself.

SD's thing is Pride. When accused, both of ducking out on his own rules, and indirectly of cowardice, his response is to double-down, both on personal danger, AND on how generous his interpretation of the rules is.
You do know the bit about each of the demi-urges having a deadly sin as their theme is entirely fanmade, right?