The horror of this wave of pillagers, raiders, rapists, and conquerors doesn’t really have a counterpart in Western Europe - indeed it ends up benefiting them, as any foe in the east rapidly has to focus his resources on dealing with Genghis and chums.
Riding out of the east, it chews up everything in its path, devastating entire nations.
In the world of medieval strategy games, there isn’t a more terrifying foe than the Mongolian Horde.