A “Browser” can’t play MPEG-2 streams.
Your Shield can play anything you throw at it (probably).
Your phone may be able to work with an MPEG-2 stream and it may not.
What’s concerning is that Plex ‘should’ be transcoding for devices that require a format change - and that’s not happening.
Do you have Transcoding Disabled perhaps?
Plex Player for Windows/Mac:
https://www.plex.tv/media-server-downloads/?_ga=2.221853144.1993529163.1575302888-1864473727.1455657109#plex-app
(the link is confusing, but it does go to the app)
Or Plex Media Player:
Are two capable and free player apps that can probably play anything you throw at them. I doubt you’ll be able to put either on that phone.