Sunshine and moonlight are open source implementations of nvidia’s game streaming protocol they created for the nvidia shield. You can use it to remotely use your computer from your phone, not just for games. But of course the primary application is game streaming. As long as the game can run on the host (sunshine) computer, you can remotely play it on the client (moonlight) device. I’ve used it to just launch steam in big picture mode and then select what I want from steam.
Going to submit my probably-not-a-puzzle-game-game: rhythm games. The game tells you exactly what to press and when you’re supposed to press it, it’s just up to you to actually press the buttons. See: DDR, Rhythm Doctor.
Note that there are rhythm games that have more decision making like crypt of the necrodancer (rhythm roguelike)