This is the game for people who don't already know it: youtube video
I am looking for theory about making an object move around another object and stay stuck to it. How would I implement something similar?
Game Development Stack Exchange is a question and answer site for professional and independent game developers. It only takes a minute to sign up.Sign up to join this community
I saw the game first time from your link, so I might be making wrong assumptions about it's mechanics. But I still think that it could be done this way.
The game seems to be all about gravity. Every block the player can walk on has it's own gravity well, and player can jump out of it if there's another gravity block nearby enough. It's simple planet-like gravitation explained here: 2D Planet Gravity
Objects sticking to the block is done with collision detection.