Their assertion that cURL is used to fetch the web page you're reading seems...misplaced. Browsers almost certainly do not use libcurl to fetch web pages. Though I do agree that libcurl is ubiquitous.
Had to over-simplify things a bit on cURL to keep this legible to a general audience, particularly in the first few paragraphs. The idea is that at some point down the stack from your request, libcurl is almost certainly involved (as a dependency, or maybe installed on your internet router, for example), not that your browser is necessarily running libcurl code directly in making the request. But yes, it's slightly hand-wavy in service of the larger point ("this is a thing you use all of the time without realizing it")