Painful Choice states:
> "Each player chooses 1 monster they control and sends it to the Graveyard. Then, each player draws 1 card."
It only sends monsters to the Graveyard, it does not trigger any effects.
Dark World monsters typically activate their effects when they are sent from the hand to the Graveyard, not when sent from the field.
Therefore, Painful Choice will not activate any Dark World monster effects.