Nvidia Shield Plex has Max x264 recommended level set to 5.1. If this is the case any auto converted High 10@X.X video will not play. It will just continuously buffer. The only way to get it to play is manually selecting a transcode option. The level needs to be set to 4.2 as even 5.0 will not work. During my testing I was thinking it was only the Android TV version that had this issue but when I tested on my Nexus Player that has a recommended level of 4.2 did I realize where the issue lies. However, Plex for Android (OnePlus 3T) has a recommended x264 level of 5.2 and it works fine even if I set it to level 5.1.
Also, I have noticed that between Plex for Windows, Chrome Plex App, Plex for Windows 10, and Plex for Android (Smartphone). They all give a 1080p 10/8Mbps manual transcode option, but Plex for Android TV only gives 720p @ 4Mbps and below for the below clip.
Below is a 10min sample clip for testing.