The governor of Otrar is a small price to pay for the safety and continuation of your empire. You admit to yourself that you miscalculated, and embrace the riches that trading with the Mongols brings to your people.
You chose a non-historical decision! In real life, the ambassadors were either all executed, or one was executed and the other two sent back with shaved heads (a very serious insult among the Mongols). This angered Genghis Khan, and he invaded Khwarezmia with 150,000 men, leading to complete annihilation. Read more about how your decisions differed here.