I had the same problem. I'm using ps4 remote play on a win10 machine and connecting my Dualshock 4 controller via a usb wireless adapter. I noticed that having the usb adapter didn't just kill sound for the PS4 remote play, but rather killed ALL audio on my PC. It turns out that the PC thinks that your usb adapter is a speaker. On the PC, go to your control panel > hardware and sound > sound while the usb adapter is plugged in. Disable it as a speaker, and you're good to go.
Credit where credit is due - I'm not the first to figure this out. Here's a link to the original solution:
http://www.tomsguide.com/forum/239538-49-xbox-controller-kills-audio.
