NetHack (or any other ASCII roguelike)
Any of the games in the bsdgames package (also rogue, which is found in bsdgames-nonfree)
For something more modern (that's on GOG), there's Tangledeep. (Not to be confused with Tanglewood, which is really a Sega Genesis game (GOG version is just the ROM packaged with an emulator), but it should be playable with a keyboard.)
Also:
Ultima 1-5 and Might and Magic 1-2 have only keyboard support, and Ultima 6 can be played with just keyboard. (Nit sure if MM3-5 can be played keyboard only.) (They may not be Linux native, but they run well in DOSBox.)
2D platformers are also often playable with a keyboard, including Shovel Knight, Cathedral, VVVVVV, Celeste (not on GOG, but available DRM-free and Linux native); the only issues are the rare game that uses analog aiming (Owlboy) or games that require lots of simultaneous button presses (Guacamelee).
I could also mention Undertale, but I've actually had better luck running the Windows version in WINE than running the Linux version. (In fact, even if playing with a mouse or a controller, there is one part where the game asks you to get out your keyboard.)
Strijkbout: Might as well try any DOS game
Many later DOS games, including Ultima 7 and on and the early Elder Scrolls titles, do require a mouse.
On the other hand, I remembered a few other games that work keyboard-only:
Bard's Tale Trilogy
Dragon Wars
Wasteland (not Wasteland 2)
Elminage Gothic