There's little or no proof I've seen that shows any significant number of people actually believe the stuff on small sketchy sites in question originally - and then the term definition got expanded to seemingly include any slightly misinformed MSM article.
The abuse of the term is infuriating because the "fake news" websites are so clear cut, there shouldn't even be a debate. Some websites just make up facts to write a story, as their main source of stories. And there's no way CNN, Breitbart, MSNBC, any of them fit the claim.
There's also a factor of people from the other side going there. Or people just curious.
Overall, I don't think that it's a good idea to use mere traffic as a way to determine influence.
The proof is that the sites get large numbers of repeat visitors and their articles get shared unironically on social media.
I mean creators of these sites make tens of thousands of dollars a month. That may be small potatoes in the grand scheme of things, but put all of them together and they make up a sizable portion of total Internet media readership.