The book is Tong Wars by Scott D. Seligman and covers in great detail the wars and conflicts in the New York Chinatown from the late 1800s through the 30s. Most of the "wars were between the Hip Sings and the On Leongs, though a strange one broke out between the Leongs and the Four Brothers Tong (the Four Brothers being a clan based tong that didn't deal with gambling and other vices).
For gaming purposes the time period from 1900-1913 seems to offer the greatest opportunities. In that time period there were a couple general shootouts that might make good skirmish scenarios. Once there was even a three way shoot out between the On Leongs, the Hip Sings and the police.
A few notes
1. While called hatchet men the Tongs were thoroughly Americanized and almost only used guns (revolvers).
2. Most wore western clothes, so regular gangsters with black hair and a different skin tone would be better stand-ins than the Pulp Chinese gang figures.