Valve's got Final Fantasy working on Steam Deck after a Square Enix update to the launcher broke it earlier this year, and the latest rollout of the experimental launcher for Proton makes it so. So if that's your MMO of choice, well, go ahead and update to experimental and experience it wherever it is that you take your fancy handheld PC.
Some other games are now playable in the experimental branch: Age of Chivalry, Chrono Cross: The Radical Dreamer Edition, Saviors of Sapphire Wings/Stranger of Sword City Revisited, Iragon: Prologue, One Piece: Pirate Warriors 4, Atelier Meruru, Warhammer: End Times - Vermintide, Star Wars Episode I Racer, Gary Grigsby's War in the East, Gary Grigsby's War in the West, Beneath a Steel Sky, We Were Here Forever, Cities XXL, Cladun X2, Succubus x Saint, Cursed Armor.
The update also has fixes for Elden Ring and DEATHLOOP crashes.
For my part, I'm absolutely gobsmacked by the idea that Gary Grigsby's War in the East and West work on the Steam Deck. I've got no idea how you'd play those... but now I've got to try.