Linux Gaming

I have steam up and running on my main daily driver ( currently endeavour OS, but I also have a dual boot to a Windows with steam also working if needed, but just about everything I'm playing lately is working great on Linux).

I have a TV connected to a older HP PC that acts as my media center. It runs Kodi on Linux mint. Both computers are wired ethernet connected. Is there a way I can stream/play games from my daily driver to my computer that's connected to the TV? Is there a Kodi add-on I could use? Do I just need to install steam on my Linux mint? I don't have a steam link device. I did some brief reading on steam remote play and it looks like that's more designed to share with others not just stream from my own account to another computer.

Currently My daily driver is actually close enough to my TV that I could even have a keyboard/controller connected to the daily driver and just stream the video if that was better. But in the future I may want to rearrange rooms, so ideally I guess it would be best to have the controller through my HTPC as well.

Any advice on how to best approach this?