Mysterious icon when pausing Apple TV app
It is the new picture-in-picture feature of the Apple TV app in tvOS 13.

Can't decide what to watch? Use picture-in-picture viewing to play two videos at once, or browse the Apple TV app while a video plays in the corner of your screen.

Details:
https://support.apple.com/en-in/HT210525


Play a movie or TV show in the Apple TV app.
Tap the Touch surface on your Siri remote to bring up the video timeline.
Swipe up on the Touch surface to highlight the icon, then click the Touch surface to select it. If you don't see the icon, you're not in the Apple TV app and picture-in-picture isn't supported.
The video will shrink to the bottom-right corner of your screen.

To watch another video in full screen while your video window plays in the corner, find something else to watch in the Apple TV app and just click play.