I think the location at which the chat and game audio mixing is happening is different for the two systems. With the 360 they at least give you the option of changing chat volume at the os level. I believe the latest xbone update allows you to do this when using kinect chat but doesn't help those trying to mod the original adapter.
I think the xbone controller receives 2 discrete audio streams - game and chat - and the mixing function happens with the adapter. Without the latest adapter it outputs both game and chat audio pre-mixed (when using the system supplied adapter) in the same output audio stream. With legacy headsets they would receive just the chat stream from the controllers and the mixing would happen at the headset or mixamp level depending on whether you've got tb or astro.
So how to trick the system supplied adapter to strip out game audio while still passing through the chat feed? May not be possible as the circuitry probably isn't setup to suppress the game feed I'm slowly resigning myself to buying the new adapter.
I am using the xbone chat adapter and turn the game volume all the way down, works great since it has seperate volume controls for game and chat