With some refinement; I could draw a lot of similarities between Skore's Annoyance concept and bugmaniabob's Psychological Warfare concept.
A Pokémon dedicated to griefing the opponent could be very interesting to see. It would disrupt carefully-laid strategies and add insult to the injury, leaving the opponent frustrated and feeling a little bit violated. A good TCG example is Life's Finale from Magic: The Gathering - not only does it destroy all creatures in play, but it then allows you to search your opponent's deck for three creatures and send those to the graveyard as well - the deck search is insult to the more direct injury.
How we could go about a griefing concept can be determined later, if either of the mentioned concepts are chosen; but it's certainly a very interesting path available to us.