I don't see the author addressing most obvious criticism. There is no definition of genius. He mentions a lack of ideas, but doesn't talk about the effect that every field is much more specialized. You won't make advances in physics on the level of Newton or Kelvin. "The basics are covered" (with all the caveats that apply to this statement). He also ignores the pure genius that went into developing computing and the internet. Or the breakthrough that made our flat screens today possible that display digital information to us in the first place, like the invention of blue LEDs as a major scientific/engineering breakthrough. There are countless examples with an immense global impact, but the names of the inventors are barely known outside of their field.
The more specialized we get the less likely everyone will learn about it in general education and thus the inventor/genius will be less renowned. That doesn't make it less of a breakthrough or less genius. The article doesn't address this at all.
Further, there are many counter examples of genius that wasn't privately/aristocraticly tutored like Richard Feynman. For his point to stand there must be more privately tutored geniuses than non-privately tutored geniuses and today less intensive private tutoring. He doesn't have data for either of these prerequisites.
I found the whole article and reasoning quite lacking right from the premise.