If you're talking about "mobile websites" in the context of a separate page/site that mobile devices get redirected to, I'm completely in agreement. Those are garbage.
But what I think they are talking about here (since I skimmed the article and it mentioned web standards), is what is commonly referred to as "responsive design" (https://developers.google.com/web/fundamentals/design-and-ui/responsive/fundamentals/?hl=en). It's the exact same website / webpage as the desktop "version", but some additional things are added to make it display / function properly on a mobile device. One such example is scaling things on smaller screens that have high resolutions to make them readable (so you don't have to constantly be zooming in and out to use the app.
And CSS does some really wonderful things now where you can display things differently depending on the size of the screen (i.e. on a desktop you might have several items laid out horizontally in columns, but on a mobile device they become stacked vertically instead)