In your text, the authors do not simply come out and say “the legacy of Khubilai Khan was…” Instead, we have to infer what sort of legacy we can attribute to him. In order to do that, we must look at what Khubilai did while he was in power.
Khubilai was just one of the Mongol rulers who ruled various empires that had been created out of what Genghis Khan had conquered. Khubilai was the ruler of the easternmost of these empires. Under Khubilai, the Mongol rule over China was consolidated. He came to dominate China and its surroundings in a way that had not previously been accomplished.
Khubilai allowed the Mongols to rule all of China. He defeated the Song dynasty in 1276 and soon eradicated all resistance to Mongol rule throughout China. He then established what is called the Yuan dynasty. Khubilai also tried to extend Mongol rule outside of China, but was largely unsuccessful. He tried to invade Vietnam, Cambodia, Burma, and Java. Most famously, he tried to invade Japan twice, only to have the invasion fleets destroyed both times by the typhoons that gave rise to the idea of the kamikaze (divine wind) in Japan.
Even though Khubilai was not able to extent Mongol rule outside of China, he was able to make the Mongols dominant within China. This led to major changes in Chinese society. Khubilai built roads to connect various parts of China. He instituted government programs to try to help the people more than had previously been done. He also supported religious tolerance. Khubilai stopped the old policy of official support for Confucianism. As part of this, he ended (at least during his rule) the old system of examinations based on the Confucian classics as a way of determining who got government jobs. Instead, he promoted Buddhism but also gave support to Daoism, Christianity, and Islam.
Thus, we can say that Khubilai’s legacy was a unified China with greater integration and more tolerance of different religions.