Here is Conway's Game of Life implemented in PuzzleScript:
I had a discussion with a friend tonight about what games (if any) were impossible to make in PuzzleScript, and we concluded that nothing is technically impossible (provided it fits into the tile-based arrow-keys-and-X-button format), although plenty of games would require unreasonable amounts of rules and/or objects. This is really just another way of saying PuzzleScript is Turing complete, as is shown by the fact that it can represent the Game of Life.
And oh yeah, since the Game of Life is Turing complete, it can obviously be implemented within itself: