GM Studio brings a powerful new set of functionality with it, called
Shaders. Think of shaders as mini programs that run on your GPU, and directly process graphics while they're being drawn.
The effect you linked in that video is known as a
kaleidoscope effect, and googling
kaleidoscope shaders brings up some neat results!Using GMStudio, you could add this shader, then turn it on while drawing your background image. Creating that effect would basically be a two step process. It's that simple!