Because it's not what the topic creator is asking for?

i just recommended an alternative solution , imho way better than playing very old games on an old pc

https://www.urbandictionary.com/define.php?term=thread%20crapping

Those are my favorite computers. Can you post your CPU model, as a celeron 1.1 is not quite enough to figure out what model it is (probably either a Sandy Bridge Celeron 847 or a N3350/N3450). I will assume your computer is made in the last 5-6 years.

Anyway, here are some games I enjoy playing in really low end devices (I use a Windows Tablet with a Atom CPU):

FTL and Into the Breach, those are really good games.
Fell Seal, this Unity game is very well optimized and will run very well.
Spacechem Engineering themed puzzle game, quite fun.
SteamWorld Heist Other SteamWorld games should work fine as well
Dragon Boy Remake of old platforming game, run very well, is gorgeous and have a dedicated button to change the graphics and sound on the fly.
Limbo Absolute classic but quite short (I tend to like short games)
Mark of the ninja GOG doesn't have a Linux version and I've played the non-remastered version, so it may be a little harder to run
Trine and Trine 2 are a bit harder to run but doable on very low graphical settings
Populous the Beginning This is one of my favorite games and pretty much any old game (80's and 90's) should run well
Shadowrun Returns Harder to run (same as Trine) but playable

Not on GOG:
Battle for Wesnoth can't even imagine the months I've wasted playing this free game

Windows versions that I tested and run well in Linux through WINE:
Guacameele and Guacameele 2 Very good games better suited to playing with a controller.

Not tested on Linux but should run well:
Spelunky free version
Spelunky HD version
The Messenger
Talisma Don't let the amount of DLC scare you, the base game is enough for a good amount of fun
Plants vs Zombies Very fun game but the Steam version will have frame rate issues. Playable none the less.

A plethora of emulated and old games that you can run on the small PC

Thank you, dtgreene. Actually I read books often, both paper books and e-reader, but sometimes it's nice to have something different; e.g., if I've already been reading for several hours and I'm tired of it, or if I'm in a relatively distracting environment, or I just don't feel like reading. That's why I posted.
ASUS E203M. Celeron N4000 with 2 cores. Intel UHD Graphics 605. I don't really remember how old it is, but your 5-6 years or a little less sounds about right.

ignore Orkhepaj, they always threadcrap.

Yeah there isnt much that can run, but most dosbox games should run, I personally recommend The Settlers 2 or Albion.

Puzzle-adventure games (e.g. Myst)
RPG (turn-based is cool)
Simulation

I want to stay away from shooters or real-time strategy since the fast, fancy mousework can get annoying if I'm stuck with only a touchpad.

I just looked up Albion. Sounds interesting.

It is, one of my favorite RPGs and done by a company (blue byte) whose other game The Settlers 2 I also love, well TS2 gets installed with DOOM and DOOM II whenever I get a new pc. I think you will enjoy it, and its here on gog, check the game forum for the restored manual too.

Any visual novel.

Old 8bit computer games (Joust, Pacman, Jumpman, text adventures, River rat, Spyhunter, Questron, to name a few)

Any console emulation of PS1 and earlier (PS2 and above it's an annoyance. Although PSP isn't too hard to do), This will give you games such as: Final Fantasy 1-9, Ultima, Breath of fire, Shadowrun, Megaman X, Super Mario Brothers, Chrono Trigger, and probably far more than i can remember.

Any PC games 2005 and before probably, although depends on requirements for video cards and compatibility. Turn down quality and almost everything to 2008 may work for you.

Any and all card games and mahjong solitaire games will work....

Then I'll mention some decent options again:
* Avernum series (aside from the Avernum 1 issue I mentioned, but you could always try the others). also Geneforge and Avadon
* Ultima 3-6
* Knights of the Chalice Demo (and probably the full version, but the demo is a good way to make sure it works)
* Nox Archaist (is really an Apple 2 game despite its recent release, so it would be run in an emulator)

As an added bonus, these games tend not to be mouse heavy, except maybe some of the Spiderweb Software games.

Worth noting that Ultima is also available on PC. Also, the NES version of Ultima 5 should be avoided at all costs; it's awful on a level that few games are; I'd compare its quality to the likes of Action 52, ET, and Big Rigs. (The other console ports of Ultima games tend to be decent, but note that Ultima 4 NES is quite different from the PC version, and Ultima 7 SNES is basically a completely different game.)

(Also, there actually is a DOS port of Mega Man X, which is actually a somewhat decent port, but you probably want to play the SNES version. This is unlike DOS Mega Man and Mega Man 3, which are different games and not that good.)

Those might not be the nicest games to play on a touchpad, however. (Minesweeper has the same issue.)

Then Eschalon, Bad Mojo, any Wadjet Eye adventure, I really recommend you The Blackwell Bundle, Primordia and Unavowed, Anachronox, Heroes of Might and Magic 3, Chronicles or 4, Undertale and World of Horror.

All of the mentioned games in my previous post should run well on your computer. Some may require a little graphic massage to run smoothy but most should work out of the box.

There are many more but those are some I tested.