How do I share Apple TV+ desktop app playback between two Macs with the same Apple ID?

I own two Macs and both sign in to Apple in the same way; basically they are nearly the same other than the name of the computers: one is MBPro4A the other MBPro4B. I'm testing screen sharing, and found that if I play a movie from Apple TV+ on (for example) machine A that shares its screen, the movie turns black on both devices when I try to view it on machine B.

I selected Family Sharing as a topic because I did not see a "plain" sharing; this is System Settings > General > Sharing > Content & Media > Screen Sharing.

Is the black screen to be expected?

[Re-Titled by Moderator]