Not sure if this is true, he got "lucky" with technological advantage of warfare (Mongol bows) compared to other nations close to him as horse archers were literally "meta" to fight vs heavy/peasant infantry same case as Crassus fighting Parthians.
You mean you only need better bows to conquer the world? What about millions of warriors already trained in battles and already winning against the biggest and most competent military force in that world (China) after hundreds of years iterated tactics and strategies?
Not really true. Horse archers were a thing before him and after him. And many of the people he thought were either horse archers themselves, or allied with horse archers, or had fought horse archers for centuries.
Yes and no Mongol Bow was a thing that was just a lot better for this era compared to rest of Eurasia especially with combination with mongols tactics and rest of the regions didn't fight horse archers much for centuries but ofc. you can disagree.
I think its up for debate how much their bows were compared to other steppe people. Since we don't know exactly how the bow making changed across the centuries.
Even if we would accept that their bows were better then some other steppe peoples, he still thought many people that for sure had the same bows as he did.
In fact, most of his life, he thought people who had the same technology, including the invasion of the Qara Khitai.
Then the Jin had allies that likely had the same bow technology. However it seems most of those allies just switched sides.
Only the Khwarazmian Empire and Xia likely didn't have significant troops armed the same way.
It could explain it if you consider how it upended stable equilibriums. If the sedentary civilizations had developed defenses against horse-riding nomads with a specific allocation of resources to that effort, and there was a sudden increase in the size of the threat vector emanating from these horse-riding nomads, it could throw their strategic posture out of alignment with their strategic needs.
In terms of numbers, it's entirely possible that larger numbers of defending sedentary soldiers are needed than attacking horse-riding nomad soldiers for the former to mount an effective defense against the latter.