Oh quite the contrary.
Indeed. That is ever and always the purpose (and the success) of the state - to steal. You seem to think this was about the Mongols vs. the Chinese.
Wrong.
The Mongols had mobilized a better way to steal from the Chinese peasants than their former rulers. Peasants vs. various gangs of thieves. Do you really think that the robbed cared who robbed them?
You think the entire point of the Mongol conquests of China was to steal from the peasants? If so, why did they end up killing most of them off?
In fact, the reasons the Mongols invaded the Jin (Northern China at the time) was because of all the abuse the Jin had done to the tribes of Mongolia (supporting the tribes against one another, and capturing tribes as prisoners and enslaving them), the Jin claiming all of Mongolia as a vassal state after defeating one of the tribes, and well, just the Jin generally being a bunch of dicks to the Mongols. The Mongols in their conquest of China certainly weren't out to just "exploit" peasants as you so readily claim, but rather, for as a result of a tangled history of abuse by the Jin.