In my opinion, really just a personal opinion, web and Internet are not synonyms. Also the Wikipedia article you mention sees them as two different things, as far as I can understand what I am reading. In a sense Internet existed long before the World Wide Web.
Internet is the underlying network whereas web is the interface used to access it (accessing webpages and services using web browsers).
The 1989 in the article refers I think to this: History of the Internet - TCP/IP goes global (1989–2010)