I must have missed where that was stated? I was under the impression that deities/majin/genies outranked demons, period. Like, only the 3 greats are even allowed to approach her without invitation (which is why Baal had to orchestrate the whole attack/rescue to get her attention in the first place), that implies she's even less accessible than the demon king himself.
ah sorry it was my own inference that the order in the demon world was:
1) demon king
2) deities
3) the three greats
so the demon world would have to prioritize the demon king's word before the deities
if it helps for you to understand my perspective, i think of the princess as a foreign ruler of a more powerful place in which her word has a powerful say and it's important to earn her favour, to maintain peace between her dimension and the demon world, but that she can't appoint a demon king herself.
the demon king has to be on the top because they stated that he was the demon world himself so in the demon world, the demon king is the most powerful.
just to be clear i am talking about the ranking from the perspective of the demon world. if i was talking from the perspective of a third dimension, then since deities are more powerful than demons, the princess would have a larger say than the demon king
edit: oh wait i read a bit more of the comments i forgot that the deities oversee the demon world T-T
i guess our only hope is for a higher ranking deity to be on the side of iruma. i did google the deities and apparently thoth is a deity but this princess is the princess of all the deities so that still may be a problem. i really hope that another deity helps iruma because this princess doesn't seem very helpful
edit again: wait i wanted to explain why i still think that the demon king is more powerful than the deities, or rather just her. now that i know the deities position, i still think the demon king is equal to or more powerful than her because her word apparently gave baal the same power as one of the three greats.
if she was more powerful than the demon king, then when baal won her favour, he should've been more powerful than the three greats.
personally, i think that the deities' role in the demon world is that they have to oversee it but that they can't interfere with it unless something that could determine the stability of the demon world is happening. i think the only reason the deities haven't been brought up earlier is because they trust the thirteen crowns to keep everything safe
to continue on my theory, i believe that the princess involving herself for baal could lead to such a large power imbalance that threatens the demon world since it's impossible to challenge her, so maybe another deity will also have to get involved.
i really can't wait to see how everything plays out though : )