You are getting answers all over the map. Let me take a shot at it.
Programming requires skills of organization and the ability to pay attention to detail. There is also more to game programming than some people think.
Questions to consider: Are you going to build your own game engine? Then you need to understand the physics of light and momentum. Are you going to try for a realistic look-and-feel for your game world? Then toss in the geometry of perspective. Learn the concept of ray-tracing, which is one of the more popular methods of building a game image on a screen. All of these things need math. Maybe not advanced calculus, but certainly you would need a thorough grounding in algebra and geometry.
If you would be content using someone else's game engine, you need to learn principles of design and layout according to whatever model is being used. Artistic and architectural design wouldn't hurt if you are dealing with a realistic city environment. Nature art wouldn't hurt for outdoor scenarios.
If you want to do actual programming then you need to understand programming structure concepts. For that, languages such as C or BASIC are invaluable, particularly the visual versions of those languages. Object-oriented programming is important, too.
One last issue: Anybody can learn simple-minded programs. However, in the computer industry, it is not that you can program, but that you can apply your programming skills to a specific type of problem. That is true whether you are a designer of operating systems, business programs, scientific programs, or games. If you don't understand the underlying problem, being the best programmer in the world gets you nothing. Therefore, don't focus on a single issue.