Good evening,
I had not been on as of late, but I guess that's good for those who do not want to unfollow people who spam posts left and right.
That said, I thought I'd go ahead and give a list of games that are under a Free Software license, both for media and game logic code. I will have a few genres to choose from, with links included. Each post will be a different genre so y'all can digest this information.
I will first start with FPS games, as they are my love:
Xonotic [https://www.xonotic.org]: AFPS made using Darkplaces, a Quake 1 (id Tech 1) engine, forked from Nexuiz Classic starting in 2011 as a result of the name buyout from Ilfonic. It features a lot of things from the Unreal Tournament games, but implements Quake movement tech (Strafe jumping, rocket jumping, CPMA, etc.). It's a nice mix of both styles, licensed under GPL-3 (for Nexuiz Classic was licensed as GPL-2 or later).
Cube 2: Sauerbraten [http://sauerbraten.org/]: A freeware game engine (with the game being freeware), but the source code to the engine is under z-lib. The engine is Quake-like, but does not implement Quake movement, and the modes are pretty decent. If you're a mapmaker, you could consider this one, as it has real-time mapmaking even with a 56k modem type speed.
OpenArena [http://www.openarena.ws/smfnews.php]: A Free Software Quake III: Arena clone, released when the engine id Tech 3 was unleashed under GPL-2. It features your normal Quake III gameplay, but with characters befitting that of a mid 2k AFPS at the time. Mods are available for it too, such as Ratmod and OmegA (both of which I've played), but the OG is where it stands for me, personally. If you liked Quake III, give this title a shot. It is licensed, since it used ioquake3, under GPL-2 if not GPL-3.
Unvanquished [https://unvanquished.net/]: A hybrid RTS/FPS made using Daemon, an id Tech 3 derivative based off of OpenWolf (A Wolfenstein engine, not a Quake one). It's a team-based FPS with RTS elements that require you to destroy the other team's teleporters (for the humans) or aeryn [eggs] (aliens). Really interesting concepts, I must say. Code is GPL-3, assets are CC BY-SA 2.5, a small bit of code under BSD, and is also licensed within the terms of the Wolfenstein: Enemy Territory source code terms.
Rexuiz [https://rexuiz.com/]: Another fork of Nexuiz Classic still keeping to what Nexuiz was, but with QOL improvements and other fixes from the original game. Started in 2015 from what I recall, and is surprisingly deep in the Nexuiz knowledge required, even with harder bots to deal with. It's licensed under GPL-3 as well.
Red Eclipse [https://www.redeclipse.net/]: A parkour-based casual AFPS with elements of both Sauerbraten and Tessaract [http://tesseract.gg/], which allows for some pretty good rendering techniques while keeping the game fresh. It's one of two Sauerbraten-based games I know of available on Steam and is Free Software, with z-lib licensed code and CC BY 4.0 media assets. The other Sauerbraten-based game is Tomatenquark. Pretty crazy as well.
If I missed any FPS projects, let me know in this post, because I know I will have missed one.