From the post:

  Everything until the tag closer </script> is inside
  the script element.

And:

  In fact, script tags can contain any language (not 
  necessarily JavaScript) or even arbitrary data. In order to 
  support this behavior, script tags have special parsing 
  rules. For the most part, the browser accepts whatever is 
  inside the script tag until it finds the script close tag 
  </script>.

Note the sentence fragment "even arbitrary data." This explains the second part of your question as to why nested script tags without HTML comments do not require matching closing tags. Similar compatibility hacks exist for other closing tags (search for Chrome closing tags being optional for a fun ride down a rabbit hole).

As to:

  why a script tag inside a comment inside a script tag needs
  to be closed ...

Well, this again is due to maximizing backward compatibility in order to support broken browsers (thanks IE4, you bastard!). As the article states:

  When JavaScript was first introduced, many browsers did not 
  support it. So they would render the content of the script 
  tag – the JavaScript code itself. The normal way to get 
  around that was to put the script into a comment ...

HTH