The Mongols may not have had cities (besides Karakorum, the capital). However, by the time Genghis Khan's conquests were under way they had a written alphabet, a
very highly organized military structure, a complex legal code, freedom of religion, and a postal system that was unrivaled until the Pony Express was established in the US. They were generally far more sophisticated than you give them credit for and their system of warfare was more than just 'tribal'. Sure, they used hit and run tactics, but a great deal of logistics and organization is required to besiege cities.
Sacking cities and killing the inhabitants was nothing new. The Crusaders did it at the end of the siege of Acre during the 3rd crusade. Khan actually gave the cities he attacked a chance to surrender and be spared.
Also, the term "barbarian" is loose, vague, and sometimes downright irresponsible when talking about history. Different cultures have viewed others as barbarians throughout history. Unless we're talking about one of these specific cases (such as the Greeks calling those north of them barbarians, or the ancient Chinese calling everyone around them that) it's a meaningless term. Would you call tying peasants to the land and severely limiting their rights and freedom to even move around a barbaric practice? Or is it just cruel or unfair?