You are quite correct.
It is very funny how people today, in the West (and since taken up by Muslims) obsess about the evils of the Crusades.
For Islam the Crusades were an ingrown toenail compared to the car crash of the Muslim invasion. Many parts of Central and SE Asia have never recovered.
The Mongols killed 40M to 60M people, something around 10% to 15% of the world’s population at the time. Nobody else has ever come close to matching that record.