A timeline of the Internet (with portraits!) from the Computer History Museum. This timeline begins in 1962 and ends in 1992 with the invention of the World Wide Web -- or, rather (though I'd say it's the same thing), with the 1992 invention of the first web browser, Mosaic, at the University of Illinois.
Here's the CLI program I used to read email at the University of Virginia in 1992, when I first started using the Internet. Again, not the web. It didn't exist yet.
Okay, here's a picture that roughly approximates how people used to interact with the Internet before there was a Web. All through text, all through a CLI (command-line interface). I started grad school in 1992 and this is pretty much what we had. This too is what that 1988 Washington Post article is thinking of when it talks about Internet.
Oddly enough, today the Washington Post has chosen to reprint a 1988 article about the Internet; that article mentions Robert Tappan Morris, the first person prosecuted under the Computer Fraud Act, whom Brittney Douress told us about today. Nice timing, Brittney! :)
Note too that this article came out well before the World Wide Web was invented circa 1992 / 1993. There weren't any GUI web browsers yet; people just used text-only terminals (no pictures, no video) to access stuff. Mostly news groups -- I'll post a picture of what that looked like if I can find one.