Ok, I feel like a slight idiot. I was rewatching The Villains Lair and I had a (probably) late realization.
So Maleficent says she wants Oogie Boogie's dice because they can control the shadows.
She says she needs to wield them because the shadows are loyal to him only.
It was at this point, I thought "Wait since when was Oogie associated with shadows, let alone being their master?"
He's not just the boogeyman, he's the shadow on the moon at night. Also since he's the boogeyman and does his work of terrorizing kids at night, he most likely uses shadows to frighten them some more.
I think the best way to describe what I'm thinking of is by showing these specific lyrics (from a certain song that I think tumblr is aware of) that I think fit Oogie's position.
So yeah, Oogie really likes terrorizing kids at night.