The following article explains what the white boxes mean on a V2 when in a game mode.
The boxes on the screen indicate what screen number is currently being viewed. Depending on which mode you are playing there are a different number of screens. The screen being viewed can be changed by pressing the menu button (the left middle button).
The most popular game mode, 'GPS + Track', has 5 screens:
1. GPS distances
3. Manual PinCollect 0-3
4. Manual PinCollect 4
5. End Round
Below shows the GPS distances screen changing to the Penalties screen. You can see the white box has moved down a space.