I am still having a gaming rig here with rx6900xt as well but way too big to get it wife approved into the living room and have no man cave to run it 24/7.
It's pretty trivial to make use of an LLM compute box remotely; in fact, most of the software out there is designed around doing this, since lots of people use cloud-based LLM compute machines. I use the Framework Desktop in this fashion
I leave it headless, just as an LLM compute node for whatever machine is running software that needs number-crunching done. So if your gaming machine is fine for you in terms of compute capability, you might want to just use it remotely from the living room with another machine being in the living room.
Another benefit of sticking the compute box elsewhere is that while my Framework Desktop is very quiet (single large fan, about 120W TDP, and is notable for being rather quieter than other AI Max-based systems), keeping my 7900 XTX loaded will spin up the fans. You may not want to have a heavy-duty number-crunching machine in the living room from a noise standpoint.