It isn't true that irreversibility per se implies an increase of entropy - or at least I can't see how it follows from the definition. (And couldn't there be a universe whose 'laws of physics' were such that states may have multiple successors but at most one predecessor--so that by the 'irreversibility' criterion, entropy is decreasing--but which had a 'low entropy' beginning like a Big Bang and consequently saw entropy increase over time?)

In any case, it's not clear (to me at least) how the definition of entropy applies to the Game of Life.