Well, first of all, your premise of inter-war influence is contingent upon the historiography of Mongol tactics up til that point. Do you have that bibliography; a bibliography of the historiography of Mongol tactics, written up to ~1936.
I don't know the rest of the world, but in east Asia, all the opponents at the time were at their OWN weakest points. They are weak by all means compared to any other earlier Chinese dynasties, not only to the Mongols of 12th century. Jin had been fighting Xi Xia and Southern Song for more than a hundred years by the time it was finally defeated by the JOINT attack of Mongol and Southern Song.My Islamic civilization was hit very hard by the Mongols as well, but there is definitely something we have to learn from them.
A lot of steppe nomads have always attacked civilized empires throughout history, but no one was as successful as the Horde. They even defeated all other cavalry based armies like the Khwarizmian Empire, which also had its roots in the Steppe. The Mongols perfected the art of war, I think. They basically fought all the strongest empires in the world, kingdoms much greater in strength, and won decisively. So I would definitely consider them unique.
I must also add that, a nomadic raider loose nothing if defeated in a fight, he can come back any time, a farmer will loose everything if defeated even if he is alive. A Chinese saying is perfect analogy "光脚的不怕穿鞋的","Bare footed is more daring than shoe wearer" because they have nothing to loose, but everything to gain. Everything else equal (strength and will), the probability theory will favour the former than later to win. That is what happened in 12th to 13th century.
Jin fvcked up everything it could on its own. Not that much external Song or Tangut merit here. Still doesn't change the fact, what large part of field battles and all key ones were lost by them open&fair.Jin had been fighting Xi Xia and Southern Song for more than a hundred years by the time it was finally defeated by the JOINT attack of Mongol and Southern Song.
Steppe nomads got their balls grabbed incredible amount of times.As siege has said, settled farming empire has too much to protect and care than nomadic herder whose only asset is his horse, bow and arrows.