Marie Antionette didn't actually say "let them eat cake," as far as historians can tell. It was something maliciously attributed to her by people that hated her, and there's an almost identical phrasing from the Jin Dynastry where the emperor is told the peasants can't afford rice, so he asks why they can't eat beef. Some people think the "let them eat cake" line was actually inspired by the Jin Dynasty story, and it is possible, but to be fair, insulated upper classes have been like that for all time. "If the poor can't afford housing, why don't they go to college?"
And Yuan China being the successor to the Mongol Empire is just history. I'm not sure why YOU'RE confused, you're on the internet, you can look it up.
Point is, the comforts of the badly mismanaged Jin Dynasty did not satiate the Mongols. It's one of the reasons the Mongols waged war and took over, because it sucked so bad. They settled down and split into several different governments after they overextended the Empire. One of which was the Yuan Dynasty.