The CSSListMenu webpart simply creates the unordered list structure with as many nested unordered lists as you require. There are some styles that are applied when a node or page is selected. It will work like the post you suggest although you will have to write all the JavaScript, jQuery and/or CSS for it and include it on your page(s).
The rendered html shown on that page you referenced
<ul>
<li><a href="#"><img src="images/home.png" alt="Home" /></a>
<ul>
<li><a href="#">Great Uncle Page 1</a></li>
<li><a href="#">Great Aunt Page 1</a></li>
<li><a href="#">Great Aunt Page 2</a></li>
</ul>
</li>
<li><a href="#">Parent Page</a>
<ul>
<li><a href="#">Uncle Page 1</a></li>
<li><a href="#">Aunt Page 1</a></li>
<li><a href="#">Aunt Page 2</a></li>
<li><a href="#">Uncle Page 2</a></li>
</ul>
</li>
<li>Page
<ul>
<li><a href="#">Sibling Page 1</a></li>
<li><a href="#">Sibling Page 2</a></li>
</ul>
</li>
</ul>
is exactly what the CSSListMenu webpart generates. As Martin stated, its all styling that makes it look/function like you want.