Wasn't it because his grandson was killed by an arrow? The RL incident involved another community (Samarkand actually surrendered after the stories of the Mongol conquest of Bukhara reached them).
The most painful episode for Genghis Khan personally occurred during a battle in the valley of Bamiyan in Afghanistan. During the battle there, an arrow struck and killed young Mutugen, Genghis Khan's favorite grandson. Genghis Khan received word of the death before the boy's father, Chaghatai, was informed. Genghis Khan summoned his son, and before telling him what happened, ordered Chaghatai not to weep or mourn.
Genghis Khan and the Making of the Modern World, Jack Weatherford
The next day Chagatai?s eldest son attempted to render meritorious
merit; bravely he attacked the city wall, unfortunately an arrow was
shot from the city wall, hit his head and he died. Genghis Khan loved
this grandson, seeing him die in the battlefield his grief and anger was
unspeakable. When the grandson?s personal guards brought his body over,
Genghis Khan threw himself over the corpse with tears in his eyes,
embracing his dead grandson. He pulled the arrow that killed him, only
to see it was a wolf tooth arrow decorated with an eagle?s feather, the
shaft was inlaid with gold, engraved with four characters, ?da jin zhao
wang? [Prince Zhao Wang of the Great Jin]. The people around him who
were literate read those words to him.
?Ah!? Genghis Khan angrily roared, ?It?s that scoundrel Wanyan Honglie!?
Leaping to his horseback he issued a decree, ?All officers and soldiers,
big and small, hear this: Anybody who is brave enough to break the
city?s defense and capture Wanyan Honglie to avenge my grandson; the
city?s women and children, jade and silk, everything is his.? A hundred
riders immediately were dispatch everywhere to announce the Great Khan?s
decree.
LOCH, chapter 37