Hi Dan. I did a little more work on this. I turned my moodleobx to just http. and connected via android phone with moodle app.
This is what I speculate, after reading through some Moodle App FAQ, and trying things out myself.
The Moodle App is meant for students and teachers, not administrators. I don't believe you'll see any capability
to manage the MoodeBox from the Moodle App. If you want your users of the MoodleBox to shutdown, or restart the MoodleBox, you'll need to have them login via a web page with a web browser with a manager or administrator level account, to see those options
(assuming you've had them enable shutdown/restart - on the web page from the MoodleBox setting admin page)
Again, this is just speculation from my reading through some forums (on the Moodle APP) and testing it out myself. I could be wrong.