Neither the original nor the Khan Academy alternative are as strictly parallel as possible:
The Tibetan system of meditation is more closely tied to its surroundings than the Zen system.
Khan Academy's most likely assumption is reasonable: we should compare like to like, either system to system or meditation to meditation. Comparing system to meditation is less than ideal. However, to my native reader's eye, Khan didn't improve the sentence.
There is a grammatical difference between "the Tibetan system of meditation" and "that [meaning, the system] of Zen meditation", although the semantic difference may seem negligible. It makes a difference whether "Zen" is inside or outside the prepositional phrase. The phrasing "that of Zen" in this context could more easily be expanded to "the Tibetan system of Zen" rather than "the system of Zen meditation". The grammar is more closely parallel, and the semantics are at least as plausible.
So, no, we can't really help you understand why Khan's alternative is the correct choice. It is too easy to argue that it is a less than ideal choice.
That being said, I still recommend comparing like to like.