No permission seems to be required to listen on a call being done:

https://developer.android.com/reference/android/telephony/Ph...

There's one permission (READ_PHONE_STATE) required for some other methods, but it is different from the permission to initiate a a phone call.

READ_PHONE_STATE is precisely what the app in question uses.

https://github.com/harjot-oberai/MusicStreamer/blob/master/a...

This used to be correct, in Android 1/2.x. It no longer is, there is no compelling reason for it to need it now that there are audio focus APIs.

I don't recall any other media player I've used requiring it.

Did they pause when there was an incoming call?

Yes