Why do they even need a View Demo button? Almost every article about CSS/JS scripts for cool effects does this, instead of just using whatever they want to demo in the blog post itself.

I didn't see it as advocating the use of the buttons just as presenting the possibility. Presumably they keep consistent buttons across the site and probably they have other button demos?

As an experimental effort, i don't see a reason why the author would change the style of the demo button in the post. The demo button here is an anchor tag with a class name and he has used that style across the site for all demo/download buttons.

Creating a separate demo page where all the html/css can be dumped looks like a better option rather than messing up with the php template.