If it's genuinely a grounding issue then why does the problem only really show up when doing certain activities on the PC? Would it not be constant?
One big difference between the games and everything else is the 3d graphics.
The video card does not use the 3d engine in the GPU for anything when watching movies, working office apps, browsing the internet.
You have described increased noise when zooming in in the game, increased demand on the video card.
Maybe the power supply is struggling to supply enough power when there is a heavy video load.
I think you also said using headphones eliminated the noise??
Where are the headphones plugged in?
The audio going to the AVR is going through the video card if not originated on the video card.
I have asked for you to look at the audio properties to find out how (the format) the computer is sending audio to the AVR.
Most audio on the computer is not 'HD Audio' or even multi channel, games are at a minimum multi channel.
If the audio is not a format the AVR can handle there may be no audio, distorted audio, or noisy audio.
If the audio is stereo maybe the buzz is low , multi channel more, and HD audio max noise.
Even if the AVR is compatible, if the option exists to try a different output format (bitstream or PCM) that might solve the problem....... Or make it worse.
I think your video card has integrated HD audio capability.
I do not know if it is completely integrated on the video card or if it also uses any other available audio resources like a sound card or the integrated audio on the motherboard.
Maybe the on board sound needs to be disabled in the CMOS setup.
Just bouncing ideas at you.
FWIW I once chased a noise issue associated with mouse movement for years, it got solved when I gave that computer to a needy relative....well it quit bugging me anyway.
Good luck, I know these issues can be very frustrating.