The West tends to demonize Genghis Khan, but the fact is that he was no better or worse than Alexander the Great. Both were utterly ruthless to those who resisted conquest, but both were benevolent and tolerant toward those who accepted their rule. The Mongol Empire actually brought peace and stability to a large part of the world; as with the Roman Empire, a citizen could safely cross the entire width of the domain without having to worry about being attacked by bandits or cutthroats. But Western society has traditionally glorified Alexander because he was European and demonized Genghis because he was Asian. Another factor was the traditional bigotry that sedentary agrarian societies have long held toward horse nomads, seeing them as primitive savages (even though nomadic pastoralism was an innovation adopted by formerly agrarian societies only after the horse was domesticated into a riding beast). In Mongolia, Genghis is seen as a national hero and founder figure much as Alexander has long been seen in the West. Although it should be noted that Genghis was a far more successful conqueror than Alexander, building a much larger empire that endured far longer past his death.
(I particularly hate the way Genghis is portrayed in TOS: "The Savage Curtain," reduced to nothing more than a mute henchman to the white Col. Green. A more accurate Genghis would've easily been the one running the show, and would've been a much greater challenge for Kirk to defeat.)