The article is not trying to make a new intellectual contribution to the existent thinking on the subject. It's to serve as an introduction for the benefit of people who may lean far too much in the direction of taking our democracy for granted–as a God-given right that can never disappear. I would guess that the Times felt like such an introduction could be useful, given the current political climate.
It's an easy and compelling introduction, rather than a rigorous intellectual treatise, in order to increase the probability that people will actually read it and thereby have something added to their perspective.
For instance, for those (such as myself) who are unaware of the Dostoevsky quote, it may be useful to see it: "There is no more ceaseless or tormenting care for man, as long as he remains free, than to find someone to bow down to as soon as possible." It may not be strictly true. But it is useful to consider that such a perspective on human behavior is, perhaps, not to be immediately dismissed as useless and ridiculous.
The way the article writer describes The Triumph of the Will is accurate (I've seen it a couple times); most people haven't seen it, or even heard of it. The reference to the "collective ecstasy" well-depicted in the film does, after all, reveal a human phenomenon that goes beyond Nazis and which it would be good for more people to understand, as a warning.
The Athenian process for protecting their democracy against populism is useful to think about, because we, in taking democracy for granted, tend not to see any risk that such a system would be useful for addressing: "When one of the citizens was becoming a bit too popular — too much of a charmer — Athenians would vote him out of the city for ten years by inscribing his name on bits of pottery. It was not punishment for something the charmer may have done, but a pre-emptive measure against what he might do if left unchecked. Athenians knew that they were too vulnerable and too flawed to resist political seduction (their complicated affair with Alcibiades gave them ample proof of that), and promptly denied themselves the pleasure. Man-made as it is, democracy is fragile and of a weak constitution — better not to put it to the test."
Again, it's useful to present such ideas to people who may not have been exposed to them before. I had already known these details about Athens. But a year ago, I hadn't, even though I studied and loved Plato in college. And I'm 62 now.