The Mongols never sent an army to the wall nor breached it…
I don’t know where they got this information.
Watch from 36:30min/sec…
The Mongols went all the way east close to the modern North Korean border and met the Manchu’s (Known as Onggud too) defending the passage. The Manchus were happy to unite with the Mongols and fight against the Jin Dynasty. That is how the Mongols went around the Great Wall.
Because, the meaning of the (Great Wall), comes from (Undefeated Wall).
If you defeat it, it is not the Great Wall…
It was basically useless because the Chinese Dynasties couldn’t finish it.
There is Chinggis Khan’s quote after going around the Great Wall.
"If you do it, finish it!"
To me the war around Great Wall is just a meme. Jin dynasty is a settled nomad so they are not so kin to defend the Great Wall like other Han race dynasty (Ming dynasty, who built most existing wall you can see nowadays).
Great Wall is not undefeated, at least not unmanned as siege in AoE4. The use of the wall is not to defend a massive invasion with many guards holding the line like Warhammer 3 trailer. It is to over watch and deter massive army and buy time for the defenders to gather troops.
They had defenders on the Great Wall, in fact, Chinggis Khan sent a small scouting party to the west side of the wall to attract the defenders so Jin would send its infantry to the other side. Which allowed him to pass the passage with less struggle.