Coming from a VG247 interview with studio co-founder Phil Tossell...

“There’s two major influences to the game. There’s the pop-up side of it and then there’s the Japanese aesthetic. The pop-up came from when we were kids; a lot of children enjoy playing with pop-up books, and there’s that kind of tactility to it, that amazing feeling of how something can be flat and three dimensional at the same time. You try to figure out, ‘How does that actually work.’ We thought that would be a good match for touch input, and so that’s what we’re trying to do; recreate that feeling.”

Full interview here