Second Sin is Gluttony.

Gluttony-based demons are pretty single minded, like Wrath demons, but they have different objetives. Instead of just destroying for the pleasure of it, they focus on devouring things and people for different reasons, since demons don’t really have the ‘need’ to feed to survive.

In Nightmare’s case, it always tries to ‘devour’ things in order to understand them and copy them. Nightmare is a machine created by demons, and for that, it was ‘born’ without any information about anything. For that, its hunger is infinite, and will try to absorb everything to understand the world, even if that means absorbing the world itself.