How may I move the pre-installed applications (such as Chess) into a sub-folder?
You can't. There are hacks that allow you to do this but really you are spending a lot of time and effort and compromising the stability and security of the Mac so your /Applications folder can be neat/tidy.

May I suggest you create a folder in which you place aliases of all applications that you want and need and use that in place of the /Applications folder and just stay out of that folder?