This is not entirely true.
The Mongols followed the laws and customs of war as they believed them to be. However, these laws and customs were not universal. A major one that came up multiple times was how many more settled peoples had no compuncture about killing a messanger who bore demands and sending their head back to the person who made the demands as a formal "no, fuck you". This was no special thing to many settled peoples; however, for Mongols messangers were offered near sacred status and killing a messanger was a massive taboo that demanded disproportionate response. As such, when such things happened the Mongols tended to eradicate entire cities involved... or stage multiple massive sea invasions that they really could not afford.
(Aside, this discrepancy in the value of messangers makes sense when you consider the difference between a nomadic culture and a settled one. In a settled culture a messanger is a dime a dozen, just about everyone knows where important places are and those important places don't move... meanwhile for nomadic peoples a messanger who can quickly and reliably deliver messages between tribes on the steppe even as that migrate is someone who's not just a swift rider, but also a good tracker and has to know massive amounts of territory to swiftly travel over it, thus it is a highly skilled and difficult job deserving special respect... as opposed to a job any shmuck can do like in a settled society.)