The idea of God’s omnipotence simply means that God’s ability to act extends to all possible state of affairs.
This ability to instantiate a possible state of affairs, accentuates the difference between what is imaginable and what is conceivable. To imagine a certain state of affairs, is not the same as conceiving it. One could imagine, that is, make as if there is a state of affairs where, for example, 2 + 2 = 5, but in reality such a state of affairs is inconceivable. To imagine that something is the case, is clearly not the same as conceiving its possibility in reality.
In other words, not all things that are imaginable are conceivable. I might imagine that a square circle exists (a proposition of make-belief), but I cannot conceive of such a thing in reality.
To ask if God can create a square circle is therefore a question that merely *imagines* a certain act by God, but there really is no such act because the state of affairs is logically impossible, it is inconceivable. God cannot make square circles or make 2 + 2 = 5, not because God is not all-powerful, but because there are no such acts to perform.
The example of changing the rules of chess to ensure a different outcome, isn’t so much a matter of cheating, nor of doing the impossible, but simply of playing a different game. Chess is defined by its rules, so if you’re going to change the rules, then you’re not playing chess anymore.
Can God make a five dollar bill so that it looks as if it was made by the Bank of Canada? Clearly not, for God cannot make something that wasn’t made by him. But again, this doesn’t say anything about God’s omnipotence, but simply of what state of affairs is actually possible.