I agree with you Danny. It's like saying the library, you don't capitalize the L. The word internet isn't a company or a trademark.
But there's more than one building called "the library" and there's no specific main one that everyone calls the Library. There's the Library of Congress, but you don't just call it the Library.
There are internets, and there is the Internet.
"Those" are probably "intranets."
It's The Internet because there's exactly one and that's its name, like the Earth, the Moon, and the Sun. Actually, there have been more moons known to humanity since Galileo pointed a telescope at Jupiter, but the Moon still refers to the same old one it always has.
I note that all the computer book publishers I work for use I in Internet, W for World Wide Web, and Website--but they are all over the map on email/e-mail, Website/Web site.
I have a speshul cheat sheet so I can easily remember which is which.
That all makes sense except I don't know why website would be capitalized. It seems like everyone has one thesedays.
No wait, I'm thinking of a Facebook page that everyone has thesedays. Whatever.
IIRC (it's been so long) it was originally e-mail, but I just write email nowadays. It's such a common word that the dash is so Last Millenium. Off-topic, but there was some article about email being a dying medium nowadays with so many people going to Twitter, Facebook and all that other
crap social media.
At least there are a few Usenet newsgroups still in use...