It doesn't address the issue that each student can learn at their own pace, which is the main part of Khan. It ignores people that had success with KA except for a quick mention. It also ignores the fact that Khan is a great teacher, and with this model anyone can learn from the best teacher there is.
It ignores the tools it gives teachers to see the progress of the students. It ignores the fact that teachers can give personalized assistance. it ignores that more advanced students can teach less advanced students.
It dismisses the achievement system while every single educator knows they work and have worked since the first teacher decided to give students gold stars. It only mentions it in passing to say that it doesn't work without offering any proof.
The truth is: There are a LOT of people who have their own idea of what the "perfect" teaching system is. When something comes around that challenges that, as with everything else, those people will try to say that it won't work. Let it be field tested, let's see the results. THEN we can say if it works or not.
EDIT: I forgot to say that it also ignores the fact that students can only advance once they completely mastered the subject. It doesn't mention that it puts the power in the hands of the students and let them take control of their own education by deciding which classes to take and when to take them. And as someone mentions, the author is also biased.
That's not the point. You can learn to solve ten math problems in a row by simply memorizing algorithms to solve the problems, rather than learning the underlying concepts. The author criticizes Khan Academy because its methods emphasize the algorithms, rather than the concepts.
There's a good bit of research suggesting that the ability to solve quantitative problems isn't necessarily related to underlying qualitative understanding. Students could benefit from teaching methods designed to promote understanding.
But yes, let us get more data, that I can always get behind.