How may I move the pre-installed applications (such as Chess) into a sub-folder? The Applications folder is way too crowded to be useful. It could be nice if I could just get the pre-installed applications that I don't use swept into a sub-folder under the Applications, named as something like "Unused Built-ins".

Then again, I cannot move any of them, nor delete them. It just won't allow me to. Am I stuck with all those mess, like an advertisement that I cannot dismiss? I just want my space, inside that Applications folder of mine, or at least I thought it was mine...

How may I move, say the Applications/Chess.app/ to Applications/Unused/Chess.app/ with the purpose of having less items in the Applications folder? Alternative solutions are welcome as comments.
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?