FNaF freemasonic/gn*stic? The checkerboards could just be a coincidence but they're in nearly every single game. Stars are also just about as common as the checkerboards too, in just about every single game, and usually hung on the roof or stuck to the walls. The puppet is striped black and white and gets trapped in a suit called Lefty, which could be like the left hand path maybe? There's a big emphasis on freeing the souls of the children from their animatronic cages, which they were put in by a character seeking immortality who runs a restaurant chain that seems family friendly on the surface but isn't when you look deeper. Metaphor for gn*sis?