One of the author's points is that the essence of history is "who & why", not "what & when," and that Khan is completely omitting that essence in his summaries.
Also, from reading the original scare-mongering article based on a single video viewed by the author, i didn't get the feeling that he was complaining about the lack of 'who and why' but rather libruls like Khan and Gates are taking over the world and throws in a irrelevant point about personalization engines in google and facebook.
As to your first sentence, one of the largest weaknesses of the entire essay is that most every criticism being applied to Khan could be applied equally to traditional education; the fact that something is tested for in class certainly doesn't make it the best thing to be learning.