Here's what @Cany has written:
Multiple in-game actions have a chance to increment the relic's counter. At random thresholds, it flashes and plays sounds. Each turn has 10% chance to add Missingno Card to draw pile. Creates visual glitch effects: scrambled name, shuffled relics, screen distortions, coastal background, and cards occasionally are randomly drawn and shuffled back into the draw pile.

Hilariously, the card shuffling thing can be abused if you really care about that stuff, as it still triggers "on draw" effects. You can create a slow infinite with just Endless Agony + Missingno relic if Endless Agony is the only card in your draw pile, as it keeps drawing/reshuffling and making copies. All you need to do is wait.

Missingno card is a 0-cost Skill, Exhaust, draws 1 card + applies visual effects. Can be used for Letter Opener stuff, etc.

Overall, the relic is basically a troll with some niche "positives".