Yes, the New World Order is definitely in every Danganronpa game! This shadowy organization seems to be responsible for the majority of the misery and suffering that the characters go through. In the first game, it's hinted that they were responsible for the Tragedy that befell Class 78. In the second game, they were behind the awful Killing School Life. In the third game, they were the ones who created the Life of Mutual Killing. And in the fourth game, it's heavily implied that they were behind the Final Killing Game.
There's always more to the New World Order than meets the eye, and it's clear that they're pulling the strings from behind the scenes. It's up to you to decide whether they're ultimately responsible for the horrifying events of the Danganronpa games.