Hide the immutability of the army list. That's an implementation detail.
Use more fluent bounds checking in the BattleMap. This is probably slower, but simpler. Easy optimization later.
Add a tolerance for drag processing on the map. At least on my hyper-sensitive touchpad, not every drag is intentional.
MainMenu uses the screen adapter class to reduce boilerplate.
Instead of passing around the entire Game instance, which may grow complex and powerful, pass a 'Director' to the screens which exposes only what is needed. Screen management. Also holds a stack of screens.
For demonstrative and testing purposes, stack the menu and game screens.