I've played around with patchbay software to manage existing audio streams. I've sent audio to both my headset and streaming software, adding a block of effects inbetween through JACK audio software, and used a similar JACK audio interface to put audio from a voice chat app to the front left and then piped it into my headphones.
I don't know the API for creating audio streams directly but as long as you can introduce enough sources and expose every audio output as a separate sink (i.e. one for your controller) it's all relatively easy.
I doubt game developers will make use of this any time soon, though. Maybe if the success of the Steam Deck brings a new life to Steam Machines?