The app can't actually play anything, video or audio.  The content never hits the app, streaming goes from the source directly to the Sonos hardware.

Facing same issue.

It’s exactly the same answer. The Sonos app is not a ‘player’, it’s a remote control that operates the system running on the Sonos devices. Since no Sonos devices have a display, they don’t process video signals. You can also see the supported audio formats FAQ.

You could Airplay the audio to most recent Sonos speakers.

I can play video podcasts in pocketcasts and get audio only, but not on Sonos. That's what I'm trying to accomplish without connecting to Bluetooth or airplay. Again, I assume Sonos does not support video file playback.

Without using Bluetooth or AirPlay 2, or an analog line in, no, there is no way to get the audio from a video played on your mobile device to a Sonos speaker. If you instead send the video to a TV, it’s relatively easy for the Sonos system to get the audio from the TV set.  

The only way forward I can see, is playing the audio via Airplay, or Bluetooth, whilst using the Pocketcast Native App for the video playback. I’ve just tried it on an iPad linked over Airplay to Sonos, it works okay and in sync.

I chose to play the audio to a Sonos Move (called ‘Moveable’) in my setup. Screenshot attached.