Thank you for providing Central Tokyo's density; it is certainly the best comparison to Manhattan in Japan. However, you are incorrect about Manhattan's density, which is 27,812.2/km²

https://en.wikipedia.org/wiki/Manhattan

and therefore still significantly larger than Central Tokyo's 15,146/km². The 10,194/km² figure you quote is for all of New York City (all 5 boroughs)

https://en.wikipedia.org/wiki/New_York_City

which is to be compared with 6,225/km² for Tokyo Metropolis (i.e., the city proper, not the greater metro area, which is 2,662/km²).

https://en.wikipedia.org/wiki/Tokyo