No. Seoul Metro has nearly double that of NYC. I have no idea how you could possibly think NYC has the most in the world. Just think of most Chinese cities, let alone Korea's capital. https://en.wikipedia.org/wiki/Seoul_Metropolitan_Subway
Actually Tokyo has much less than Seoul. You're counting railway stations, not subway stations. There's a large difference. Though the water is quite muddled, the easiest way is to actually look at the maps of the differing cities.
I was actually very let down by the metro of Tokyo compared to other Asian cities. Probably due to my high expectations.