jQuery code is embedded in the demo I have downloaded, and the goal of the demo is to show how to use the tool. I have tried to remove this code and then tabs do not work.
All you need to do is change the className of the old selected li element to "" and the new selected li element to "selected". That doesn't require jQuery, but if you remove the code without replacing it with a non-jQuery alternative, of course it's not going to work. The tabs, though, don't depend on jQuery.
Nothing has been proven, the article in question is about how to STYLE the tabs to get the rounded corner design, not how they function as tabs. That is a secondary concern.
The use of jQuery was to provide the functionality so you can see it in action. If I felt the need I could easily recreate the tabs on a series of pages that do not require javascript at all.
The only reason this might need javascript involved is if the tabs are changing content on the page without loading a new page, such as swapping out divs in a container.
I believe you are confused about design versus function.