Although I think your organization is not that bad, its a very basic structure and not that scalable. If your Project is getting bigger, you won't stay that happy.
I would recommend you to have a look at the variety of MVC frameworks out there which do all the routing of your page request and help you to keep your project maintainable. They also help to split logical code and your layout.
If you wan't to stay with that structure you should at least change some parts of it:
I may misunderstand you but you should do it all the same way. Not using functions called from your switch statements and on the same time redirect directly to reg.php in my opinion.
switch($page) {
case "register":
//inlude file or call function
break;
case "register_submit":
//inlude file or call function
break;
case "logout":
//inlude file or call function
break;
case "order":
//inlude file or call function
break;
case "login":
//inlude file or call function
break;
}
Then maybe make an "assets" folder or you can call it whatever you like on the same level as your systems folder and put all your css/js/image files in there.
But I stilly recommend you to use an MVC framework. Personally I'm using Codeigniter. But there are several good frameworks like for example Kohana.