It is probably a little bit of a complication to apply the 20th century abstraction of GDP per capita to this time in economic and technological development?
While China was leading edge for most applied science in that time, the relative advantage of technological superiority on the battlefield is much less for the twelfth and thirteenth centuries than since the era of steam power and low cost steel production.
No. Gengis Khan had an alliance with the Uyghur state which gave him access to an advanced civilization to supplement his powerful military state whose combat doctrine at that time was unrivaled on the planet.
Also the Mongols didn't conquer China in one big bite, the Song had a heavy hand in the downfall of the Jin.
Mongol culture was crass and crude but it wasn't the equivalent of a failed state and at the end of the day military technology was at close to parity besides the odd fire arrow
Mongols were nothing more than 1 group among several competing warlords states but steppe confederations were a constant plague against northern China for centuries. The Great Jin were in fact the result of earlier conquest by tribal peoples instigated by Jurchen just as Mongols were the tribe which created the Mongol Empire but readily co-opted the manpower and organization of many tribal peoples.
It would be more fair to compare the Mongol conquests to the Roman conquests where both began as small states and rose to power based on alliances and absorption of neighbouring peoples.
If you're comparing just population, it'd be something like this:
Mongol Plateau - ~700,000
Jin - 53.5 million
Song - ~60 million
Xi Xia and Kara Kitai also added several more million. Obviously nomads could mobilize much larger (up to 20%) segments of their population than sedentary societies could, but it was still stacked against them. There isn't going to be reliable population and economic data though elsewhere the world.
The Roman comparison doesn't work because none of their foes were particularly strong on a historical level. China was disproportionately advanced, rich, and large in the medieval era. This did, however, assist the Mongols after their initial victories in China when they began to expand westward. When you've evolved in the most competitive environment and learned from the best, everything else becomes a lot easier. This applied to the steppe unification wars as well. The anti-Mongol coalition in 1204 likely had over 60,000 cavalry.
Previous nomadic empires could win battles or raids but couldn't make conquests. The Xiongnu, Gokturks, and Uighyr khanates could threaten Chinese dynasties but could not conquer anything of the important areas of China. The Manchurian tribal peoples, who had access to excellent equipment and much closer contact with China, did better. The Jin did manage to conquer about half the Northern Song with their tactical superiority, which was extremely impressive. Their advantage was timing, attacking the Liao and Song after a long era of peace. Earlier, with the Liao at their peak and with much larger forces than the Mongols, could not make consistent headway against the nascent but blooded Northern Song. It was too difficult for them to besiege Chinese cities, and even though their strategies were very advanced for the period, that wasn't enough.
There really is no analog in history and I don't know how to make a modern analogy. Zimbabwe is too unified, isolated and surrounded by weaklings, so it wouldn't have had the chance to learn from the most advanced nations with the greatest military tradition. Chinese captives and defectors, and their integration, were critical in giving the Mongols the edge they needed. Modern Syria might be slightly more accurate, but forming an analogy across 800 years is never simple.
It wasn't just that the Mongols won. In order to conquer what they did in that timeframe, they simultaneously attacked every state bordering them on multiple occasions. That basically should not be possible.
In those days, because of really slow transportation system, technological limitations of weapons and the long time to train a professional army as well as high upkeep, there was a limit of how much a kingdom could field at any time and the rate they could replenish that army.
So if the Mongols win the initial engagements decisively, they could rampage through the enemy territory and further slowing down mobilization and destroying military structures for recruitment. Basically, the Mongols would fight increasingly lower quality troops as the war progress until the only army the Chinese could field would be armed peasants sith low morale; all this as the Mongols themselves gained more experience and became more acclimated to the region. There was a massive difference between a well drilled, well trained, weathered Mongol veteran and a soft Chinese peasant with a sword or a spear. In an army structure, 1 Mongol could be worth 20 Chinese peasants; so even with a large population, the Chinese had no chance of raising a large enough peasant army to defeat the Mongols in time. The army they could raise over and over would never be large enough to reach the threshold where they could do significant attrition damage to the Mongol horde.