Would be interesting to see if this model works for every subject and with every lecturer, or if there's something particularly good about Khan's lessons.
I'd definitely argue that a large portion of the success is due to Khan's teaching ability. There are plenty of other videos on youtube explaining the same concepts, but Khan's are the best I've found.
I think there are several factors that make Khan great at what he's doing. To begin, he's a very smart guy, a MIT grad electrical engineer. While there are plenty of equally intelligent people in the world, not many of them are teaching K-12. On the other hand, he isn't arrogant or condescending, which tends to be off-putting to someone trying to learn something. Instead, he often makes it clear that he doesn't know everything. Then, there is his obvious passion about the subjects. Just watch some of the videos, and it becomes clear he is truly amazed by this stuff. This inspires the person watching to want to understand the material so they can also be amazed. He is also rather amusing, casual, and informal in his presentation, without wasting too much time or coming off as desperate to make the student laugh.
About the style of the videos, 10 minutes works very well. It's just enough time to cover one small concept. Plus it has the huge benefit of the 'just one more' effect. Similar to games that lead to 'just one more turn' and then it's 4am (Civilization), it's much easy to watch just a few more 10 minute videos than to start watching 40 or 60 minute video lectures.