I have a setup where I use a HDMI-over-Ethernet extender [0] to play games in my living room from my homeoffice desk setup in the bedroom. Funnily, the computer and TV are just 1m apart, but separated by a wall and I didn't want to drill (it is a rental). Luckily it is new construction, and all rooms have CAT7 ethernet outlets (most rooms even have two). I use a female-to-female ethernet coupling in central fusebox to bridge those cables together (they need to be directly connected, switching is not possible). So the signal travels around 30-40m over ethernet even though the devices are literally back-to-back against a wall.

HDMI-to-Ethernet extender cost around 50€, but is limited to 1080p@30, 720p@60 or 1080p@60 in "low quality mode" (macOS lingo) - which is enough for me. Low quality mode is still good enough for games. As you just read, my computer is a Macbook Pro so it is not AAA games anyway. I think there are now extenders that can do 1080p@60 on regular HDMI quality.

[0]: https://www.amazon.de/OREI-Anschl%C3%BCsse-Splitter-Extender...