As far as I can tell, aTV 4K does not play back 4K@60fps at all. I have not managed to get any 60fps 4K clips to play back, I only get the "not supported format" message on the screen.
Your software doesn't like your media. Could be a million different reasons from incompatible video and/or audio formats, medias encode is too complex for the software and/or hardware, etc.
Keep in mind the player software still needs to support a format/codec regardless of whether the hardware can natively or not.
This 4k 60fps h265 video will play on the ATV4K using Infuse 5. I'm using a NAS with no server/transcoding software to verify all the decoding is being done on the AppleTV via software/hardware.