I'm beginning game development, and I started by reading Michael Morrison's Beginning Game Programming, which teaches how to develop a game in C++ using the Win32 API.
I've had a lot of trouble with things I don't have any experience in (when I shut down my program, the process still runs, should it do that?), and something came to mind-- what if Win32 isn't even relevant to game programming? The book I read is around 3 years old, and the software industry seems to have changed a lot since then. Is it still relevant today?
If it isn't relevant to game development, could someone point me to an API that is relevant to game programming?

win32 is sort of the basis, the lower level end of c++. In my opinion it's about as fun to program as vomiting after a rollercoaster, you hope it was worth it. However it gives you a lot of freedom, but if you want I'm sure there are some libraries that do the rough work for you.

I'm not familiar with the book, but I expect that it still has a lot of good information. In particular, anything it has to say about the concepts behind games, like object modeling, rendering, AI, &c. should still be relevant.

If the book is strictly win32 API, I imagine you're stuck with GDI and PlaySound. These are fine for learning; you'll pick up concepts that apply more generally.

You're going to run into limitations, though, especially in the graphics and sound department. For more complicated multimedia, you'll want something more powerful, like DirectX, or OpenGL and OpenAL if you want to target more than just Windows machines.

Modern games are usually made with OpenGL, DIrectX, XNA or something else than win32. My advice to you is to not worry about win32 and pick up either opengl or directx