Personally with your current breakdown I would put Unity in the game engines category. I am assuming the distinction between an "engine" and a "library" is that the former is more or less self-contained (you don't fundamentally need to go look for anything outside the engine and are in fact discouraged to do so, as everything you require is already there) whereas libraries are meant to be used separately to achieve some functionality. A good way to identify game engines is to look for built-in scripting tools and content creation tools, which is a sign you're dealing with an engine and not just a library.
Other than that I don't see what is wrong with "Game Libraries". It gets the point across - libraries that games can use :) though SDL and SFML are usually core libraries since they can handle most of the work on their own (nobody says "I got my splash screen working - time to add SDL!", they just say "I will use SDL for this project" from the get-go). I would guess Assimp, XNA math, are probably more representative of game libraries in this sense.
I am trying to fit "framework" somewhere in there but I really don't think it's necessary, though it depends how precise you want to be about it.