This looks like a Windows form. As such, I would suggest that you have a background thread that runs in a while loop and handles all of the movement/update logic of your game. The complex part will be managing state between the Windows form thread, and the game thread. You will need to ensure you're event handlers for button clicks etc. that update game state are doing so in a thread safe manner, as they will be on the GUI thread. The game loop thread will need to update state on the GUI, which will require what is known as marshelling, because only the GUI thread is allowed to access controls that exist on the form like buttons, etc.
The topics of thread management, thread safety, and marshelling I'll leave to you to research.
This assumes it's some sort of real time game, rather than turn based. If it is turn based, then you don't really need a game loop. You could accomplish the same goal by using a state diagram and purely event driven design.