The qpwgraph workaround works in the matrix clients as well, but passing media audio into a WebRTC stream meant for voice is not ideal. Any decent client is likely to heavily filter out background audio (which with a game would be a lot of the ambient soundscape), and the audio would in some cases end up mono.
Broadcast-box is on the simpler side, if self hosting. If not, there is a public free-to-use instance here: https://b.siobud.com/