Although I am Irish, and a fan of celtic Missionary work, my username is taken from the other great missionary church of the Dark Ages, the Assyrian Church, also known in the West as the Nestorians.
The Christian nation referred to in the letter was probably the Uyghurs or Naimans of whom a significant number were Christians when Genghis Khan conquered them. It was the Uyghur script Genghis adopted.
The problem is, although your monk travelled to China to meet the emperor, it was not a Chinese emperor he met but a Mongol. The reason the monk was able to travel to China is because the Mongols had conquered most of Central Asia and China too allowing trade to move across the Silk Road. The Uyghur was adopted by the Mongols for their Mongolian language which was previously unwritten, but Chinese was a different language continued to use its own Chinese characters.
Here is an example of Uyghur script which as you can see is very different from Chinese characters.
. . .. . Guyuk Khan's Stamp