From the introduction:
ENGINE is a game atop another game.
To play ENGINE, you must have and play either Apocalypse World by Vincent Baker, or one of the many games derived from it. Playing with one of its derived games with ENGINE will take a bit more work, as this game is designed with Apocalypse World in mind. It should work, though. Caveat: If you can use the word "dark" to describe the game, it should work.
Just play the game as normal, but add the provided Principles. Then, once done, play ENGINE. Play it right after, or play it another day. Either way works.
From the back cover:
ENGINE helps you to tell a story of renewal. It helps you to explore the causes and ramifications of the things that occurred in the original story.
It does not reflect on all Moves, or all Principles. Not by far. But this is a foundation. If you choose to build more Moves, we'd love to hear about them.