The claims are very exaggerated, but a small nation with a relatively small army turned to psychological warfare above all to secure their borders and/or recent aquisitions. The deaths in Khwarazm certainly achieved their aims. After the Shah's defeat the nation still had the capability to raise an army large enough to threaten Mongol borders. As to the total of lives lost to his conquests, I would not even begin to try to work that out

......Orda