Stephen, thank you for the information. I will use your experience to further refine my statements. e.g., I will perform further testing and compose a more concise statement of the operation.I just disconnected myself from the internet as you described. I was able to play all my downloaded videos, both personal and the ones I had purchased from Apple on my iMac (High Sierra). I was able to play all my Handbrake-generated personal videos on my Apple TV 4, though I was no longer able to play downloaded purchased iTunes videos.
I could mirror my Mac to my Apple TV and play the purchased vids that way.
I also tried this with my MacBook Air running Mojave. Same result.
I previously tested using Windows and iTunes 10.7.x with a third-generation Apple TV (A1469). I will retest with macOS High Sierra and iTunes 12.6.x, etc.