Is it possible output audio from a laptop to a desktop using an HDMI cable so the desktop can then process/play the audio input from the HDMI cable?

I'm mute, but I would like to talk while I stream. To do this, I wish to use a TTS program while I play. Since it would be obnoxiously inconvenient to switch windows while gaming, I'd like to hook up my laptop to my computer so that my laptop may be used as a dedicated TTS device. I'd like to send audio from the laptop through the HDMI cable into the PC, and from there it would go through OBS to be streamed. I only have an HDMI cable at the moment.