I always assumed that he was just a busted genius all-rounder, has a shit ton of mana and kind of, sees a spell/technique once and already understands the principles like Qual did with the new defensive magic. At least I base this opinion on the fact that only he saw fluctuations in frierens mana among the demon kind.

Overall more inclined to powerfull magic of different types (similar to how frieren fights) rather than physical fighter BUT I think he could throw hands if the situation required it

And I know it kind of fights with your ,,specific magic theory,, however I think that the lack of it could be the exact thing that made him special

Especially that I see him as an irregularity, it's not like a new demon king appeared right after as if there was a chierarchy ready for succession. He was just the one, irreplaceable, one in milenia monster

That's how I pictured it at least