“Shuffle Track Play” is not usually a VIDEO function.
Any DVD player that has that feature is likely to only enable its operation if an AUDIO CD is being played in the tray.
I don’t know how one would create a DVD disc with a “Random play” built-in command.
At the end of a track, there is usually placed a command that tells the player to either “go to X” or “hold.”
I don’t think there is a common “go to ‘random’ track” command.
If anyone else has seen this, please post.