Is it? I think it shows some chutzpah to write such a long article defending such a thesis, but it's also completely wrong and thus not very good. We already had this: It was called Killer Websites or later Flash pages. We killed it with fire when the web professionalized.
There are two forces at play here: On the one hand you have those print inspired designer types, boosted by the possibilities of modern browsers. On the other hand you have the usability requirements and the dictate of the form factor: If you do a mobile website you need a very simple grid, responsive for bigger screens yes, but the focus is on structure and content. Free placement of stuff according to print design ideals of magazine cover pages is completely useless there, the phone screen is too small for that anyway.
What we end up with is the current design: Very formalized pages for the most part, with lots of possibilities to experiment thanks to evolving browser capabilities while keeping the standardized structure. This will lead to further evolution of what is a modern design, but I doubt we will see a complete new paradigm anytime soon - as long as technology remains as constant as it was the last 10 to 20 years. Foldable phone screens might move the needle a little, if they ever come down from the uber-premium price segment vendors target right now and don't turn out to be a useless gimmick
One thing to keep in mind: Yes, web design is new, but because we already had print design before it adopted very much very fast. This is not a completely new field that still has to match what humans actually need, it already took that from existing research and practices. That's why it could evolve and settle down that fast, and that's why the article is wrong in predicting the next grand revolution, that happens to need their website builder.