There are lots of different philosophies on unit testing. Unit testing is more of use during development, so that if you want to make changes you can make them without worrying as much your change will break something you do are not thinking is related. Basically it would be writing other methods that call your internal game methods with different parameters and check to see if the results are as expected.
You do not need to unit test for the app store - chances are you have been testing the game all along as you have developed, and that user testing is a lot more important for getting something released (as it means it probably will not crash) and also of course that makes for a better game!
One final note, if you are thinking about unit testing in the future there is a downside. It can also mean more work when re-writing code as you not only have to change your original code, but also related tests and make sure the results they are looking for make sense. For a single person that overhead may not make sense; it is more helpful when many people will be changing the same code.