As with your question about the legacy of Khubilai Khan, this is a question for which the authors of your text do not give a direct answer. Therefore, we must look at what the Mongols actually did and try to infer from that what their goals were. I would say that the goals of the Mongols were to hold power over their empires and to benefit from that power by exploiting the resources of the areas that they controlled.
The Mongol homeland was not a very rich place. The Mongols themselves were relatively poor, nomadic people. This gave them a strong economic incentive to conquer. This, along with political and military power, was their main goal for conquest. In addition, the conquests help to fulfill the desire of the Mongols to fight without causing them to fight among themselves.
We can infer that the Mongols held these goals by looking at the things that they did. Most importantly, the Mongols did not attempt to impose their own cultures or beliefs on other people. For example, Khubilai Khan did not ban Confucianism or try to impose Mongol beliefs on the Chinese. Instead, the Mongols essentially kept to themselves and allowed the Chinese to do more or less as they wished (in their culture and society) so long as they remained obedient. The Mongols did the same in the Ilkhanate, allowing the Persians to run their own government and tolerating all religions, including Islam, Judaism, Christianity, and Buddhism. In China, the Mongols forbade intermarriage with the Chinese, wanting to ensure that they remained distinct.
From these things, we can see that the Mongols were not trying to impose their culture on the lands they conquered. Instead, they tried to make sure that the lands remained obedient and that order was kept. This allowed trade to flourish, enriching the Mongols. Thus, we can say that the Mongols’ goals were to dominate their subjects politically and militarily so as to ensure that the Mongols would gain economic benefits from their conquests.