Are you explicitly looking for competitive multiplayer games? Single player shooters like Prey, or the BioShock games, might be able to fulfill what you’re looking for. I like Helldivers 2, as well. It’s not slow per se, but your fighting AI and not people so insane reflexes are far from important. It’s coop but very worth your time.
I’ve personally been using a raspberry pi with a Bluetooth mouse and keyboard. I just run jellyfin in Firefox and navigate with the mouse - the keyboard rarely ever being necessary. I was able to increase the icon size so it’s acceptable on a tv and bookmark any streaming websites I use. It’s certainly not as clean as using something like an apple tv, but it’s serviceable and I don’t have to fiddle with plugins like when I tried Kodi. Honestly though, apple tv probably fulfills what you’re looking for like others have said.