The templete is called that because it uses a new type of Access files that's called "web database". (If you have Access 2010, you'll find that when you create new database, you'll be prompt to create a "standard database" or "web database". More on that here and  here.)

So if you goal is just to create a whatever SharePoint website, just export the schema there and recreate the same structure on whatever database engine you like and it should work the same.