This game is quite different from Conway's Game of Life because it's not deterministic. During a turn, cells will rely on Math.random to find whether to move or divide; the direction that the cell move into is also randomized.
I agree, you can call it cellular automata if you want but it is false advertising to draw any comparison to Conway's Life. Still, it is fun an interesting but I would have found it more compelling if it didn't have a random component. That's part of the magic of Conway's life that complex results arise out of simple, deterministic rules.
"There have been many competitive versions of Life written over the years."
Mistaking "Conway's Game of Life" for "Cellular Automata in general" can produce sub-optimal results. The same thing that makes Life so interesting is that from its simple rules, extremely surprisingly things result. In some sense it is in the class of maximally interesting "suprisingness" as it is Turing-complete. But this same surprisingness and the wolly, humanly-unpredictable way it manifests make it almost entirely useless for game playing.
The general idea of cellular automata can be turned into game form, but you're better off defining your own rulesets, which can produce things like http://chir.ag/stuff/sand/. I also remember playing a game that actually resembles the linked page, but where each player moved a mouse cursor around, the cells tried to follow each corresponding player's mouse cursor, and the various blobs would eat each other. Probably one of the most clear examples of a game I god good at (relative to my opponents) and couldn't even begin to verbalize my strategy, even though I had one.
The Powder Toy, more or less the state of the art in falling sand games now, has a raft of Life rulesets. I found it quite interesting to pit them together; they have no particular rules for directly interacting with one another, but the way they take advantage of life and death and empty space nonetheless can produce some fascinating interactions anyway.
Assuming the RNG is a deterministic random number generator, then that should make the entire game deterministic? Given independent runs, the decisions that each cell takes should occur in order, and therefore achieve the same result.
You don't know what the starting internal state of the RNG is, so no you can't predict it. The starting internal state being secret is what gives PRGs their security.
