Emby Server 188.8.131.52
Apple TV App 1.2.14
I deleted all the logs, started Emby server, then tried to play the file in question on Apple TV. Many (20) ffmpeg logs were created after an attempted playback time of around 5 seconds, all with the same error: "Error initializing output stream 0:1 -- Error while opening encoder for output stream #0:1 - maybe incorrect parameters such as bit_rate, rate, width or height".
Attached are one sample of the many Apple TV ffmpeg logs and the single ffmpeg log for successful playback on browser. Let me know if you need the server log too.