I’m skeptical if Genghis Khan was really a vegetarian. He would have lived in the 1100’s? 1200?
GK vegetarian? VERY unlikely.
The Mongols were pastoralists. Their diet was about as animal-based as that of the Eskimos. Meat and dairy.
They even drank the blood of their horses, sometimes mixed with milk, on long raids.
On the steppe there was very little a vegetarian could eat. Little or no agriculture.