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Team Fortress 2 [Community Servers!!] is a great game with lot of playstyles, weapons, and maps which makes each new round a different experience. However Valve cares too much about Counter Strike to care about the DDOS attacks and bot crisis makes me wonder why they keep casual mode server up? Community servers are fun and pretty much the only way to play TF2 right now. Contrary to my name, I actually main pyro and soldier instead of scout, like my name suggests.

Quake III Arena, and of course on a device that it's not made for like the 2007 Nokia E90 or 2009 Motorola Milestone

Maybe just code your own games.

Slingshot game from Stardew Valley

There's this cool block game called "ClassiCube". Not sure how good it is. I hear it has a good community and a very prolific developer. You should consider checking them out on your favorite video game console.