What this article failed to mention is that the world wide web has something that the internet doesn't: content. The internet is a network of networks, but nonetheless a network. It provides connectivity. It does not have content but allows access to it. By contrast, the fundamental feature of the web is (hyperlinked) content.
An attempt at some one line definitions:
The Internet: a network of networks allowing access to a great array of content, most significantly the World Wide Web
The World Wide Web: a collection of hyperlinked content, hosted in servers spread across the world, accesssed via the Internet