First, that is a really poor citation, but let me just take it at face value. Here's what the article claims (from qualitative research btw) does have an impact:
-frequent teacher feedback
-the use of data to guide instruction
-increased instructional time
How many of those are not even doable by Khan?
By the way, when I say 'class size matters' I'm not saying that 'large class sizes aren't effective.' I'm saying 'smaller class sizes are more effective than large class sizes.' We all know learning can happen in pretty much any environment. The question is how to maximize that value. The fact that you can learn in the stanford AI class is very far away from answering the question 'is that the most effective way to learn.'