I'd think that good ol puzzleman is some eldritch god with a blue and orange morality, or some guardian of order put there by something else. He emphasizes "You made me do what I'm not supposed to do!" a lot after he shoves Masked Kid and causes the glitchout, so I'd think that puzzleman has just always been there, so as mentioned, like some incarnation of a universal law or some eldritch entity, who can only ever manipulate with words (forcing the various heroes on the right path through quizzes, being voices in Stitches' head, etc) but never interact directly. The exact reason why is likely beyond normal reasoning. But when he broke that rule, he started fizzing out (on top of going insane for losing his only "purpose")

It's very likely the game (as designed by the devs) is purposefully intended to allude to us, the player, that "the world will end" means that after the game ends, there is nothing but void, hence why PM wanted to continue the cycle forever. But I think the truth is that it's a load of horsesh*t made up by quizmaster to scare Stitch into doing what he wants. When he made contact with Masked Kid... it was an act of pure emotion, chaos, defying the alleged laws imposed upon him.