I just tried this with my Sharp Roku TV. I have a computer connected to one of the HDMI inputs and am currently using it as my work monitor. I received the same error, but as soon as I moved off the HDMI connection and back to the Roku screen, it then because available.
What that tells me is that Private Listening through the app is only available when use the Roku TV as a Roku player or OTA TV reception. It can't be used for private listening when using one of the HDMI inputs of the TV. When I switched to a broadcast station, the sound came through my phone no problem. As soon as I switched back to the computer, the sound was no longer available.
Dan
Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.