I think that looks decent, just some general suggestions:
- An abstract base class Menu that handles the Game-variable for you.
- Learn to use references and shared pointers of various types.
- Keep interface, game mechanics and objects fairly seperate, look up the basics of MVC, model view controller.
I'd suggest that you don't worry too much about design like this, it's highly likely that you will realize that your design doesn't work or is suboptimal down the line after building the rest of the game, and then you can rewrite it at that point having learnt a lot more when building the other subsystems.