Mark Brown released a new Game Maker's Toolkit, which you can find here. This is largely a response to that video.
The basic premise is that the "Nintendo approach" to level design is to take one core challenge and follow the same set of progressive difficulty enhancements: safe introduction, slightly less safe thing, unsafe thing, then a few dozen twists to change the challenge somewhat.
He uses the design of Donkey Kong Country: Tropical Freeze to offer a counter-example, where ideas and themes are largely mixed together in clever ways. For example, sawblades don't just threaten you, they also carve out platforms. This level has leaves and horns, etc.
... Those are the same design philosophy.
There are differences in implementation, sure. Mostly because the mainline Super Mario games are extreeeeemely tired.
Tropical Freeze seems to be more creative in their theming, using a broader variety of themed challenges and better spectacle setpieces. This is probably because they A) have better technology and B) aren't exhausted and tired like the mainline Super Mario games. Other Mario games like Paper Mario, Mario Galaxy, and Mario Sunshine tend to have more creative levels with strong theming - comparing their best levels to Tropical Freeze's seems more evenly matched, with levels where island rise from the water, exploding volcanoes, collapsing buildings, and so on being far more common.
It may sound like I think the video is baseless, but I don't think that's true. I simply think he's comparing bad and good implementations of the same level design philosophy.
It's good to discuss pacing, and the limits of theming. Unfortunately, that's not how the video was pitched, at least not to my ears. It sounds like he's talking about things "Mario doesn't do". Mario doesn't do them in the mainline games because those are tired, not because they're not part of Nintendo's arsenal.
I'm not arguing that the basic idea of themed rising challenges mixed with spectacle is good or bad. It's one approach, and it's a fairly well-understood and robust approach. There are lots of other approaches with other priorities, and they're not mutually exclusive: an open-world game would have a hard time sticking to this formula, but they can certainly use the formula as a foundation to pace the player's entrance into a new area with its new themes and challenges.