No, they are writing about DNS, which is in the core of how the Internet works. Including the Web, yes, but virtually nothing on the Internet would work without DNS.
A lot of things wont work, but you still can't say Web and Internet are the same thing.
I also think it isn't fair to nitpick the article for it.
But the article doesn’t conflate the web and the Internet. The DNS root servers are necessary for the operation of all the Internet, just like the article says. Not just for the Web.