I don't have that problem. It fits the entire screen on my Moto X Developer Edition.
I think I've got the same thing on my Galaxy Tab 2. Do you mean how the left and right side are just empty black space? It's the same in http://arstechnica.com/gaming/2015/11/we-put-fallout-4s-mobile-pip-boy-companion-app-through-its-paces/ of the app, so I just assumed it was intentional. Kind of a waste of space, but it's probably so it works with the collector's edition pip-boys. You know, all 200 of them.
I downloaded it for iOS and you have the option to choose between display mode and full screen. Display mode is for when you stick it in a Pip Boy. Maybe an update will fix that for you guys.
Weird, that option isn't available on Android. If I click the gear in the lop left corner, the only option is to change the connection to the game.
On a related note, does anyone have a way of changing the volume of the in-app sound effects? It's a little loud.
you certainly don't want to leave it on 'Animal Friend' for an extended period
I wonder more a about the offline mode. Does it work via USB debugging and cable plugged into the phone?
As it looks right now, I won't use the app, due the active internet/W-Lan connection it seems to require.
Also: Same Screen Issue here:
Samsung Galaxy S2
Android 4.0.4 (Custom Firmware)
Rooted: Yes
I have the same "issue" with the screen being fixed at the 4:3 looking format making it black on the sides, even if I pick fullscreen. I thought it was by design though. Using a HTC One S.