I was under the impression that Genghis Khan was an invader while Kublai was more of a patron of fine arts; but reading Wikipedia it mainly mentions his campaigns for the Mongol throne and the unification of China.
Did he actually contribute significantly to world culture, and if so in what ways?
The most important thing Kublai Khan did for culture was to found the Yuan Dynasty, which sought to rule what Genghis had conquered. It initiated trade between east and west, cross-pollinating ideas and culture. Specifically in China, this resulted in advancements in the arts - painting, calligraphy and poetry combined into a new discipline similar to Persian art, and poetry likewise was introduced to theater, along with western instruments, in zaju and sanqu.
Pax Mongolia pretty much re-established the entire Silk Road that previously languished due to wars and inconsistent tariffs.
The cultural impact of Marco Polo is strongly linked with Kublai Khan as this was who Marco Polo was said to have visited as a high point of his Asian journey.
What the Mongols may have taken in lives and bubonic plague is perhaps offset by a long step forward in international trade and globalisation; or at least accelerated thereby.
In two words, Marco Polo.
This was a teenaged Venetian who travelled with his father an uncle to Kublai Khan's China. When he returned to Venice in his middle age, he brought back Chinese "apps" in paper currency, astronomy and navigation that helped the Venetians and others in their naval and trading endeavors, as well as more accurate maps of the land routes between Europe and China. Polo is sometimes credited with bringing back cultural influences, such as Chinese noodles for Italian spaghetti, but that is less well documented.
Kublai Khan also founded the Yuan Dynasty, which lasted nearly 100 years, and ruled over it for its first twenty-odd most peaceful and profitable years. During his reign, he improved ship and canal building, and trade generally, particularly internal trade. The art of ceramics (porcelain) also made a new high during the Yuan Dynasty.
