I’ve been experimenting with the Game of Life for decades, it makes nice visuals for techno music, and you’re right, it demonstrates something about the nature of our world. Also, I love the way you’ve framed in terms of it representing certain mode of existence.
The Game shows that even the simplest systems are unpredictable. If anything, it demonstrates the possibility of “intelligently designing” the universe as virtually impossible, at least with the idea that humans were going to materialise several billion years down the track. And the Game also shows that the laws of physics are capable of producing wholly unexpected results.