Completely incorrect. The Mongol social structure did that without religion. Like most nomadic peoples, inheritance rules split the ownership amongst a leader’s sons, fairly equally. This is because they had people and herds, not land (hence, nomads), so it was the most sensible way of doing it.

This, mixed with the fact that Russia and the Middle East are thousands of miles away from the Mongolian and Chinese capitals made it inevitable that a leader on one side of the empire would ignore their overlord on the other side. Thus, the empire would fracture quickly (and pretty much did as soon as the family ties to Genghis Khan were loose enough).

Neither statement is true. You can’t fanatic your way out of a weak economic base for long and plenty of non-religious people live happy fulfilling lives.