Computer engineering integrates several fields of electrical engineering and computer science required to develop computer hardware and software.
if you adopt this course you will become more familiar with many hardware and software aspects of computing.
Computer programming is about logic and algorithms. here you will be taught about programming languages and how to program something yourself. (I think this course is needed for Game programming.) Game designing using soft wares is not something that you should take. You will not get money. But if you chose to be a game programmer then the company will give you a lot of money since LOGIC has more importance.(Some Game programmers earns more than $200000 per year)
Software Engineering is the study and application of engineering to the design, development, and maintenance of software.(I don't know much about this)
Computer science is a practical approach to computation and its applications. it can be divided in to a lot of subcategories including computational complexity(deals with execution mainly--how much time, space does an algorithm require to execute etc), programming language, graphics etc