Is it only when playing this specific game, or do you have that in general, like when playing Steam games or modeling something in Blender?
For me it sounds like a hardware issue. The GPU is pretty old (age-wise, ignoring performance). Some electronics will degrade over some time and just stop working. That's my guess.
Also, two 4k-monitors sounds like torture for a card like this :D
Maybe install/ live-USB a completely other distro on a second drive and replicate this situation. Use default Ubuntu, Mint or Fedora, they have a different DE/ compositor and some other different underlying stuff.
If everything works fine, you know it's probably KDE, and if you have the same issues, it's a hardware problem and you have to repair/ replace something.
Don't forget to update me on this situation :)