Responses
Basically it I think. He doesn't feel bad for the murdering, and probably doesn't feel guilty or remorse for what he did but logically knows he hurt mc even if he cant feel the emotions of it all. He knew about the antidote way before but yeah, was willing to die after mc yelled at him like that j think.
Also.. he does get a bit better in the redemption arc-y bit. Slightly.

I think the reason why the king let himself die was because he felt some kind of remorse?
Like he wronged his sex partner. And he understands his a murderous mother fucker. But like.... There's no way he could apologize for what he did. He's a proud sadistic king who probably felt justified with everything he did. But he may feel some type a way that he pained his sex partner.
And the unnamed demon or whatever he is, it's the only thing he wants. To watch the King slowly die. So he granted that.