[gwd]

> Why have two people linked the same youtube video as if that's some kind of response to a graph?

Because the "but" in the sentence implies that leveling out means there's no problem. Filling out the missing pieces:

> South Korea is invoked [as an example of a country that is in major trouble], but it seems like the population there has almost perfectly levelled out at just over 51m [, which implies it's reached a stable and sustainable equilibrium.]

The video predicts not that it's at a stable plateau, but that it's reached the apex of its curve and is about to begin plummeting.