gavra_at_work: You are right. That is one of the many problems with this analogy. Nonetheless it works for most people because it is an example of knowing a result in advance while keeping free will intact.
The real answer to your question is to forget about analogies and learn the Meforshim. As other people have pointed out it is a long, complicated Sugya and doesn’t lend itself to a coffee room discussion. Nonetheless, I’ll give you something to chew on, but it really isn’t an answer.
When you look at Rav Dessler’s discussion of free will, you see that he talks about a war where the battle line moves after each battle. If there is true free will during the battle and the Nekuda of free will can change as a result of the battle, then it follows that Hashem’s will is CONDITIONAL. In other words, Hashem says if you succeed in this battle, then you will advance into enemy territory. If you fail, the enemy will advance while you retreat. But either way, the next battle could be in one of two different places. Going back to the chess analogy, this means that Hashem’s Yedia is that he can see all of the possible moves you can make and all of the possible counter moves he can make all the way to the end of the game. It is not that he knows in advance what you will do.
The problem with this idea is that in fact Hashem does know in advance what you will do. However, for the purpose of illustrating the concept of Hashem’s conditional will, the analogy is a good analogy.
The “game” of life is played on a “board” that has sequential moves where time is our greatest gift. Beings that aren’t physical can exist above time and this means they know the future and therefore can’t have free will. We however, do not know the future and therefore we can be rewarded or punished based on our sequence of “moves”. I agree that for understanding this point, the chess analogy is completely useless. If you think of an analogy for explaining this point, please post it.