I know that my monitor is 4K and my download speed is far above what should be necessary for maximum quality.
Going back to the start of this topic, you were talking about the blocky playback using the Vimeo app on your 1080 Amazon Fire TV Cube. You also said the playback on the 4K monitor was fine. The 1080 TV will be streamed the downrezed 1080p video at a max of 7Mbps per the Vimeo resolution page. It could be lower. Your download speed might not be the bottle neck. That's just your terminal connection from your provider to you. The bandwidth elsewhere along the path through the Internet to the Vimeo server may be less. There could also be an issue with the Vimeo app on the TV not handling a faster bitrate. I don't know.
The clip you posted Monday clearly shows compression artifacts (most likely the result of compression to a lower bitrate by Vimeo), especially in the area where you have the greatest motion. You also said that clip was now showing the artifacts on the 4K monitor. That takes the onus away from the Vimeo app on the TV and points more to a slowdown in the Internet path to you or possibly an issue with the Vimeo servers. Could it be possible that your Internet provider is setting Quality of Service parameters that may throttle down certain types of traffic? Again, I don't know. I was seeing it on my desktop so I think it may be more aggressive compression on Vimeo's behalf. Just guessing.
Vimeo says that you should specify variable bitrate encoding. Are you doing that?