I know I'm a bit late to this thread, but Mr. Churchill, do you mean to tell me that a movie I downloaded legally using the authorization code included with my physical Blu-ray copy was somehow ripped using inferior software? Are you really telling me that Universal Pictures doesn't use "quality software"? Are you also telling me that Apple themselves is also using inferior software? I couldn't watch even the titles I downloaded from them. I got the same "This content cannot be played because its format is not compatible with Apple TV." message.
Readers may notice I'm referring to the problem I had, the same one as what was described by the other posters, in the past tense. I figured out what MY problem was. This isn't to say this is the answer for everyone here. Mr. Churchill, while you "wasted" your time with the guys in this thread, you failed to suggest the possibility that there might be another issue. For me it turned out to be network related.
I had my ATV4 plugged into a HomePlug powerline adapter. Due to the layout of my house, and spotty Wi-Fi coverage, I've previously depended on these in some rooms. In this case, the ATV4 was not getting the bandwidth it needed in order to play the files I had on my Mac mini in the other room. Instead of Apple writing code into tvOS to lead the user in this direction for troubleshooting, it apparently takes the "one message for all problems" approach.
I'm calling you out on this Mr. Churchill, because you have a "Level 10" status. I'm not suggesting that at Level 10 you should have all the answers, but I am suggesting that at that level, you should have a better attitude towards those of lower levels.