I've done a bit of digging on this, but can't seem to find anything recent. Apparently this combo worked in the past, but a shield TV update broke compatibility (sound only plays out of the left speaker) Has this been fixed in an update since then? I also have an older Sony android TV but that doesn't work at all with the headset.
I guess my thinking is I can replace my Raspberry Pi (rasplex - works with my headphones) and Steam link with one device, but just need to know if these headphones work properly first...
I have this same setup and it works. Try connecting the headset to the ps4 and download the headset app and set the profile to standard. That's what I did last time and it fixed it. My shield tv is updated to the latest version.