"Li Ying wanted to ambush them [Mongols] on the way [back from China] with his forces (which had grown to several tens of thousands)."
"When the Mongol army besieged Zhongdu (Beijing) in 1213, Li Ying, Li Xiong and a few other Jin generals assembled a militia of more than 10,000 men who inflicted several defeats on the Mongols."
What would happen to the Mongols? If they aren't that affected, what would happen to the Jin? The Song?
I am afraid, Genghis Khan dying 14 years earlier than in OTL would butterfly away the Mongol World Empire as we know it.
He might have been remembered as one more guy, who united some wild nomad tribes for a short period of time and disturbed his neighbors.
The Mongols had had a
long history of killing each other and loyalty to a khan or a bloodline had never been their characteristic feature.
Butterflying away Chengizz Khan so early is like butterflying away prophet Muhammad some 14 years earlier - the changes in mentality of their peoples wouldn't stick.
In OTL 13 years after your supposed PoD the aging Chengizz Khan leaving for his last campaign did not appoint his successor. It was his (principal) wife who came out and publicly demanded him to choose one of his sons as his successor. The point here is that she did not ask, she
demanded. That was kind of breach of etiquette, but she was pretty sure that her husband might die any minute; and the moment he dies - his sons (and actually his brothers and nephews) immediately start killing each other in the most brutal way.