The wiki says 179 (1/10th your number).[0]
There is also Toei Subway, JR East trains, Minato-Mirai, ...the list goes on. 2100 may work for the entire metropolitan area of greater Tokyo.
In any case, the city is massive, extremely well connected by public transport, and services millions of people daily without delay.
I could probably believe the 2,100 number if you include all the surrounding prefectures that are in the broader Tokyo area, and if you count stations multiple times for each railway operator services them (it's not uncommon for a single station in Tokyo to be run by three or five different companies).
> There are around 136 individual rail lines in the Greater Tokyo Area, and between 1,000 and 1,200 railway stations depending on one's definition of the area.