I'm not disputing that. The difference is that the "populated parts" of Seoul comprise the entire habitable area of the city, which is what makes public transit so affordable even for those who live in the outskirts.
There is no low-density "sprawl" in or around Seoul. It's all high-rise apartments and condos until you abruptly hit some sort of obstacle (like a mountain). It makes little difference which counties and districts you pick. Of the 25 wards that make up Seoul, the one with the lowest population density has 25K per sq mi. The highest has 74K. So the peak is lower than NYC, but the standard deviation is much lower as well. In other words, there's less diversity of living arrangements.
A random residential area in the outskirts of Seoul looks like [1].
A random residential area in the outskirts of NYC looks like [2].
[1] https://www.google.com/maps/@37.564524,126.846419,3a,75y,186...
[2] https://www.google.com/maps/@40.706197,-73.754464,3a,75y,172...
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