The way I understand why this is possible is due to the fact that Game of Life is Turing Complete, and can therefore construct a Universal Turing Machine capable of simulating itself.
Well, kinda. This is an intentionally visual representation, but it could just have been a rules set that builds a series of gates that create a computer that does the calculations for the game without actually rendering it. Basically seeing the game isn't necessary, though this is pretty awesome.