macOS How can I make a simple game with muliple windows?

How much programming experience do you have? Do you know objective-c? Based on your question, it sounds like you might be trying to run before you walk. In that case you might want to take a look at the guides at the top of the macrumors programming forum to help get started. I apologize in advance if my assumption about your level programming knowledge inaccurate.

I haven't read that book, and I'm a bit surprised it doesn't cover the differences between a document-based application and a standard Cocoa App. I think the project you're thinking of sounds fun and interesting, but is more complicated than you probably realize, and might be something you want to put on hold until you grow your knowledge/skills.

Just to answer your original question though, for something like a game, you're going to want a standard Cocoa App. The document-based app is designed around the idea of multiple windows that are different instances of the same prototypical document. for example, an image editor, a text editor, a web browser are all designed around the idea of having the ability to have several document windows open. The standard Cocoa app is more like iPhoto, iCal with single-window interfaces (although they can have auxiliary panels and helper windows etc.). That wasn't the most articulate explanation, but hopefully it was enough to explain the difference in general terms.