At least with regards to the original question, your point isn't a rebuttal. That we can make an abstraction of the game and then operate on that abstraction ju

At least with regards to the original question, your point isn't a rebuttal. That we can make an abstraction of the game and then operate on that abstraction just means the meaningful/informative portions of the game (within the context of playing the game) are contained in the abstraction. In fact, that just is what an abstraction is: taking only the necessary features for some particular context.