I have been in touch with Applecare and we could not resolve the issue, to date. We even did a hard restore via iTunes and a laptop with a USB-C cable.
Starting to think this could be an issue with TVos.
The issue is isolated strictly to playback of movies "rented" via iTunes on the ATV4. I use my iMac to order and download the content. My network is fast. The iMac is connected to it via wi-fi. The ATV4 is connected via ethernet. I have always used Home Sharing to stream content from the iMac to the ATV, and with my old ATV 3, this worked fine. And when I swap-in the ATV 3 now, it still does. But when I connect the ATV 4, "rentals" do indeed appear on the screen to be selected,, as they should, but once selected, will not play. The screen goes black for a few seconds, and then the display goes back to the menu screen.
NOTE that ALL OTHER CONTENT, photos, "purchased" movies, home videos, music, podcasts etc. play fine. I even purchased a movie last night, just to test things. Worked fine.
So what is unique about the "rental" transaction? I believe it is the fact that rentals require ongoing two-way communication between customer and Apple to determine when rental period starts/expires. I can't imagine a hardware issue in the ATV4 that would ONLY affect the rental feature and nothing else.
Applecare suggested I take the unit to the Apple Store. There is no Apple Store anywhere near me so I may end up mailing it back....this 3-day-old piece of gear that is probably fine but has buggy software inside it.