I've got no real life experience with the American mafia since I don't live in the USA let alone NYC, but going by what I read I don't see any other criminal organizations challenging the mob either. Probably that's largely because there's little conflict of interest, but I don't think the mob is disrespected by other gangs.

As far as their lack of violent activity goes...even though it's very unlikely they're gonna whack you these days, the fear that something "might" happen is still more than enough for most people.

I live in a border region in Europe and this area has registered activity from at least one major Ndrangheta clan from San Luca, a mafia clan from Agrigento, a Turkish clan from Trabzon, an Albanian clan from Shköder, a Dutch Traveller clan from North Brabant, an outlaw motorcycle group and a Moroccan gang based in the Netherlands. None of these organizations have killed anyone in this area, but nobody is willing to find out what would happen if they would cross them.