Leaving the Dragons out of it: Mongols vs. Dothraki
The history of the Mongols is fascinating and I would strongly recommend the podcast Dan Carlin's Wrath of Khans Sometimes truth is more impressive than fiction. The podcast was free, but is now $1.99. It is well worth it. Buy Dan a coffee and download the podcast.
That is a well choreographed scene...
I will give Game of Thrones this, it did a decent job in showing that Dothraki charge and capturing (at least for a few minutes) what a Mongol calvary charge would have been like. The Mongols were expert horse riders (think circus rider experts) who could shoot arrows effectively from the back of a moving horse. The Mongols did not need dragon airpower to win.
Drogon was very impressive in the Spoils of War
EBL: Which is better?, Game of Thrones as a 1995 TV Show, European Steppes and Wrath of Khans, and Women of Marco Polo Rule 5
Dragon vs. AC 130 Gunship?
Dragon vs. A-10 Warthog?
Atlas Obscura: Moon Cakes and the Mongols