I'm not sure if these games will fit your list, especially since some of them are standalone mods for commercial games - those ones are made to run on fan-made recompiled versions of the original game engine, for Doom, o r Duke Nukem 3D or whatever(where the original game engine's source code was very kindly released for free by the original game's creators - I wish many more companies would release their game's source codes). As a result, you don't need to own the original game, you just download the one archive/.zip file, unarchive to a folder on your hard drive, and run it.
But all ofthese games are really good.
First person shooters:
Ashes 2063, a superb standalone mod running on the Doom 2 engine, it's massively popular, and deservedly so.
https://www.moddb.com/mods/ashes-2063
Alien Armageddon, a huge standalone mod (running on the Duke Nukem 3D engine) that contains so much content, such as other playable characters with their own weapons, many new single player and multiplayer mods (and bots to play against in the multiplayer modes), RPG/upgrage elements, a co-op mode, etc.
Link removed, in case the game contains pirate code or data.
The AMC Squad, another great game running on the Duke Nukem 3D engine.
https://www.moddb.com/games/the-amc-tc
World of Padman, The, a really pretty first person arena shooter (using the Quake 3 engine).
https://worldofpadman.net/en/
Blade of Agony, a really good World War 2 shooter running on the Doom 2 engine.
https://www.moddb.com/mods/wolfendoom-blade-of-agony
Total Chaos, a first person survival horror game. I've not played this one (horror games don't appeal to me), but by all accounts it's excellent, so I thought I'd mention it here. It runs on the Doom 2 engine, but you wouldn't guess that from looking at it.
https://www.moddb.com/mods/total-chaos/downlo … /total-chaos-10
Third person shooters:
Psi-Ops: The Mindgate Conspiracy, a great third person shooter where you use both conventional weapons and mind powers (telekinesis, mind-control, remote viewing, etc) to fight a corrupt organisation whose leaders and main agents have various mind powers.
https://www.majorgeeks.com/files/details/psi_ … conspiracy.html
2D arcade adventures:
Klass of 99, A great remix of the two classic ZX Spectrum games Skool Daze, and Back to Skool. Note that the Windows version can't use full screen mode, for some reason.
Windows download: https://bitglint.itch.io/klassof99
DOS download: https://dosgames.com/game/klass-of-99/
Driving games:
Carmageddon Special Edition, a fan made compilation with many new levels and vehicles. You can either play the game as a racing game, or instead win the game by destroying your oponnents, Demolition Derby style. You have to run over pedestrians (it's not exactly a realistic game!) and also hit barrels to gain more time (the race ends when your time runs out) and you can pick up various useful/worse than useless temporary power ups.
Note: There seems to be a bug/glitch with this game - it has problems if its folder name or folder patch is too long or contains spaces. To get it running properly run it from a really short patch, such as C:\CARM
Link removed, in case the game contains pirate code or data.
2D shooting games:
Grid Wars 2, a really enjoyable game.
https://worldofstuart.excellentcontent.com/grid/wars.htm
Puzzle/Strategy games:
Augmentinel, a very good clone of the classic 1980s game The Sentinel.
https://simonowen.com/spectrum/augmentinel/
Windel, a simple but good version of the word game, Wordle.
https://www.dialup.net/windle/