The HDMI Forum, responsible for the HDMI specification, continues to stonewall open source. Valve’s Steam Machine theoretically supports HDMI 2.1, but the mini-PC is software-limited to HDMI 2.0. As a result, more than 60 frames per second at 4K resolution are only possible with limitations.
should be able to with hdmi arc, not sure 100% tho but it seems like you could tell the projector where to send the audio, i know you can with tvs and hdmi arc. worst case scenario you do dp in to the projector and hope valve has stereo or optical out to go into reciever