I've been gaming on Linux exclusively for 3 years now. So. These are all proton-tested-and-approved. Though a couple (especially the old ones) require a bit of tinkering.

• Pillars of Eternity I and II -- Slow burns. cRPGs. Get very good, but take a while to get there
• Tyranny -- Same developer, also a cRPG, but gets to the point faster, and in fact can be finished in one weekend. Do note: It's an "evil campaign" type of RPG.
• Pyre -- A fantasy basketball game with a Visual Novel on the side. Very touching story, made me cry twice. And the gameplay is no slouch either, even if I kinda suck at it. (... Though when you lose the games you don't game over, the story just changes)
• Wolfenstein the New Order -- FPS set in an alternate history where the nazis won WW2, where you play a resistance fighter. Very enjoyable action, and it always feels good to blow nazis away.
• Dishonored 2 -- Stealth-FPS/Immersive Sim where you play as an assassin-princess who can turn herself into a horrid tentacle monster. Also a nice story.
• Enderal: Forgotten Stories -- Skyrim Total Conversion title. Very surreal and trippy story. Pushes the Skyrim engine to its absolute breaking point to realize the developers' vision, and doesn't always get there.
• Fallout: New Vegas -- I mean, if I didn't bring it up, someone would. New Vegas is a flawed and messy game, but it is just about competent enough that you are fine with it being less-than-ideal in the name of getting to the story.

If old games & emulation are on the cards --

• Terranigma (SNES) -- What if Legend of Zelda... But you are literally creating the world by doing your quest. It's nuts. I love it.
• Legacy of Kain series (PS1, PS2, PC) -- Very flawed gameplay on all of them (each in its own unique way)... But it is legitimately one of the greatest tales ever told through gaming. (note: It's also edgy)
• Prince of Persia Sands Trilogy (PC, PS2, GC, Xbox) -- This little trilogy of games from the sixth generation delivers in both elegant platforming gameplay and entertaining storytelling. Does suck that they are from a time that game devs thought subtitling your cutscenes would make your skin fall off (or something. No games back then had subbed cutscenes and it sucked)
• Paper Mario/Mario & Luigi series (Nintendo machines) -- Comedy RPGs about the Mario characters (duh). Very well written, especially Thousand Year Door (GC/Switch) and the original Mario & Luigi (GBA/3DS). Story is as vanilla as you'd expect, since it's Mario, but it is worth it for the comedy imho