For me it was his intense facial expression and the finger steeple. It's trying way too hard.

That’s part of articulating yourself intelligently ;)

the context for "How the top %1 communicate" here is: "in our current media environment".

I made it all the way down, and I think it's not a bad way to start. If you're allergic to fluff, here's the core separated into three levels of skill (OP's levels, not mine):

Beginner:

    - Problem – state a relatable problem that you’ve observed or experienced before.
    - Amplify – illustrate how that problem leads to a negative outcome if it is not solved.
    - Solution – state the solution to the problem. 

Intermediate (kinda like the high school 3-pronged essay):

    - Start with the main idea (the key conclusion or recommendation)
    - Support it with key arguments (usually 3-5 key points)
    - Provide detailed evidence (data, examples, analysis)

Advanced:

    - Problem and amplify – your introduction should state a relatable problem
    - Cross-domain synthesis – note patterns or concepts from your other interests that help support your argument.
    - Unique process or solution – give a list of ideas or steps that best solve the problem you introduced at the beginning, solidifying the transformation. 

If I had to sum it up, it's this: beyond knowing your audience, people like stories. Stories are the affordances of information, like the handle of a door. Stories have arcs, and in many domains they go something like this:

  - Here's a problem.
  - Why it matters.
  - Here's addressing your objections.
  - Here's a solution.

All the different levels have an arc. It's not the only arc out there (hero's journey is another one), but this one is pretty typical. All in all, it's pretty basic advice for communication and storytelling. But it's the basics that are so crucial that most of us don't practice. I meet lots of people who don't really have a structure when articulating anything, even topics they know well. A bit of structure, and can probably go a long way to help them in their careers. Anyway, this is a nice reminder. Just ignore the preamble fluff.

I gave the author a bit more benefit, made it through the part where he describes how some guys impressed him by talking in a way that sounded smart, straight to the interjection that many people subscribed to his whatever in the last years.

Then finally I was convinced enough that this did not sound in any way like what I think intelligently articulated communication sounds, and I also gave up.

He goes on to gush about Jordan Peterson and says you should think of your best ideas like tweets.

I'm not saying OP is wrong (I could not tolerate the article enough to finish it) but it's an oddly abrasive way to present a viewpoint.

I quit reading after he recommended carving out 1-2 hours of writing practice every day.