Here are my suggestions. They should all be playable on your computer and are early 2000s vintage. You can find a lot of them for free here in the Internet Archive. I’m not sure how well most of these run on Linux Mint though, but a good way to check is to see if they’re playable on the Steam Deck since that’s a Linux based OS that’s popular.

Deus Ex 1 - Classic futuristic sci-fi FPS/RPG. Advanced technology, conspiracy theories, human augmentation. All wrapped in an awesome plot. Definitely try this one out if you haven’t yet. There are sequels, but none of them are as good as the original.

Unreal Tournament - Arena FPS that has excellent gunplay and runs on a potato. Can be played with somewhat decent AI as well. Has lots of well designed maps.

Half Life 1 - Classic FPS. It’s expansions, Half Life: Blue Shift and Half Life: Opposing Force are great as well.

Morrowind - a classic RPG set in the Elder Scrolls universe. Rich story and lots of ways to play it. Lots of mods out there as well.

SiN Gold - Action FPS with a rather bombastic plot.

No One Lives Forever - Funny espionage themed FPS with great dialog. Also has a sequel, No One Lives Forever 2, which has memorable lines like “oh no, more medical bills” when you shoot a henchman. You should be able to find these for free since their source code got released and was abandoned by their developers.

Soldier of Fortune - standard FPS where you play as a mercenary in various countries. Also has a sequel, Soldier of Fortune 2, which should be able to run on your computer.

Draken: Order of the Flame - Third person action game that was very much overlooked at its time. Had great on-foot combat mechanics and you could fly a dragon and engage in aerial combat. To this day there hasn’t been a game that really does this as well as this one.

Age of Wonders - Turn based strategy with a lot of depth in a fantasy setting. Its direct sequel Age of Wonders 2 should also be playable and has an excellent soundtrack.

Hearts of Iron - Real time 4x grand strategy set in WWII. I think its sequel, Hearts of Iron 2 is the best in the franchise and it has some expansions that add alternate timelines.

Diablo 1 - the original hack-and-slash isometric RPG. Also has a direct sequel Diablo 2 which should also be playable.

Neverwinter Nights - Isometric RPG, control a small grip of adventurers in a DnD setting.

SimCity 4 - A great city builder when Maxim was at its peak.

Need for Speed: Hot Pursuit - Racing game that puts you also against the cops.

Star Wars: Racer - Now this is podracing.

Descent: Freespace and Freespace 2 - Excellent plot driven space sims. There aren’t many of these out there, and these are some of the best in the genre.

Grand Theft Auto: San Andreas and Grand Theft Auto: Vice City. Both are great GTA games.

Mafia - third person story driven action set in the 1920s. A remaster was recently released last year, but the original should be playable.

Age of Empires 2 - classic RTS, the remaster should still be playable on your hardware as it isn’t too demanding.

Return to Castle Wolfenstein - ever wanted to fight techno-Nazis? Now you can in this FPS.

Assassin’s Creed 2 - one of the best in the entire franchise. Action third person, but without the RPG mechanics of the later entries.

Tom Clancy’s Splinter Cell - great this person stealth game. Has the best dynamic lighting of any game in its era.

Fear - horror FPS, has some jumpscares but also good gunplay.

Grim Fandango - A classic story driven adventure game set in the mythological Land of the Dead. This one runs fantastically on the Steam Deck so it is definitely playable on Linux.

StarCraft - another excellent RTS

Jedi Knight: Dark Forces 2 and Jedi Knight: Mysteries of the Sith - first/third person lightsaber action games. You might be able to run its sequels, Jedi Outcast and Jedi Academy as well.

Factorio has an extensive demo and should run well

Half Life 2

Doom and Quake! When I used a potato PC as a daily driver the thing I played the most were boomer shooters. The source ports for both games are pretty amazing nowadays!

Minetest, Mindustry

RimWorld, I guess? It should work and has infinite stories to tell.

Suggest some explicit content free game ideas.

I’m sure there’s plenty of free porn games…
Oh right, you probably meant games without explicit content

Looks like Factorio should run on those specs if the graphics card supports DX11

Undertale / Delta Rune Sorry, missed that this is the freehames community.

Want one of the best crpg of all time, still standing the test? Get Ultima VII. There should be a bunch of ways to play it, I believe, even if it’s from 1991 or so.

I’m sad I’ve scrolled through more than a page and no one suggested Tuxracer.

If you’re into zombies, Cataclysm: Dark Days Ahead. Has a bit of a learning curve though.

I’m surprised that no one has suggested classic point and click adventure games other than Grim Fandango:

• Day of the Tentacle / Maniac Mansion
• Full Throttle
• The Monkey Island series
• Sam & Max
• Police Quest
• Simon the Sorcerer
• Leisure Suit Larry
• Thimbleweed Park

Someone mentioned Ultima VII. If you’re into RPGs then check out the Wizardry series, Blade of Destiny, Betrayal at Krondor, and Dungeon Siege. Oh, and Final Fantasy VII (original) and VIII.

Also take a look at the GoG catalogue for games released before 2010 or so. Most non-AAA games should run on your system.

I’ve had a similar setup for quite some time, but you didn’t mention what GPU you’re running, also since you’re running Mint, are you comfortable with Windows games (through wine/proton) and emulation?

Solitaire?

Didn’t see this was free games community, sorry!

I haven’t validated that these have low enough requirements, but they are very not-demanding games in my experience. You can also use Proton to run them on linux if they don’t have a native version.

Baba is You - simplistic graphically, but immensely satisfying mechanically. Amazing puzzle game.

Celeste - gorgeous graphics and buttery smooth controls, a platformer that is encouraging and supportive all the way through but ranges from “easy as pie” to “hard as nails” as you progress. One of the most satisfying games to complete every level for. One of the best soundtracks ever. Trans rights!

Fez - another simple-ish at face value platformer game, but this time with puzzles as the main thread instead of action. Super satisfying puzzles and an amazing soundtrack.

Omori - an RPG which eventually deals with some heavy subject matter but does so tastefully and maturely. It’s a splendid story either way you spin it, and lots of fun.

Undertale - same as above, but shorter and more “punchy”. One of the best soundtracks in gaming, and a cast of characters you’ll come to feel like your family. It’s quite subversive for the genre, so it’s a fun experience. It has an episodic sister game which is still in the works.

Void Stranger - a block-pushing styled game, but incredibly subversive for the genre. Gorgeous visuals, great soundtrack, and some truly mindbending puzzles. It gets super hard, but it’s also super satisfying to beat.

Stardew Valley - cozy farming game, really just oozing passion and love from the developer(s). Lots to do, many unique people to meet and things to see. Pretty graphics and stunning soundtrack. Fall in love with an NPC, marry them if you want. Or don’t do any of that. Make your own fun in this one, there’s a bunch of aspects to get into.

Citizen Sleeper - perhaps on the edge of games I’d recommend, performance wise, but absolutely a must-play. A gripping, beautiful sci-fi story, told in a tabletop RPG style. You won’t be able to help falling in love with the rag-tag character cast, and shedding a few tears along the way. It’s very down to earth but makes me long for the stars at the same time.