Recently I've become a bit obsessed with the idea of changing perspective as a gameplay mechanic. It probably started with Fez, and since playing that I've come up with dozens of prototypes based on the idea of the same data/situation meaning something different when viewed differently.
For example, I like the idea of a social base-building game where you can put other people's bases "behind" yours. So any gaps in your base are filled by the rooms in that spot on their base. Since rooms often need a lot of effort and support infrastructure, it's possible to put in rooms that would be impossible for you to build. In turn, they could put your base behind their base and, by coordinating gaps, you could both have a much more interesting base than either alone.
I also like the idea of a game where you continue to tell the story by folding or flipping the pieces of the story. For example, if the story begins with a castle, you might fold the castle to reveal the narrow, tall tower the princess is at the top of, or unfold it to reveal the knights and king of the castle proper, or flip it to show the dungeon and the evil vizier...
I also also like the idea of this book: panorama book (via Jenny Winder). The idea that the pages/elements you aren't using can fade forward or backwards to become support elements seems brilliant. More than a simple aesthetic, this also allows you to control which elements can simultaneously be in focus. This is important: normally, if you have two dozen elements that all play a role, the programmer has to take into account the many things they can do with each other, and the player has to decide to try to mate up various pieces. But if it is organized such that specific pieces can only come into focus with specific pieces, you can reduce the explosion of complexity and maintain an orderly flow without chaining the player down too much.
I'm going to try to think about how you might make story games using these techniques!