All theorems applying to this class of games apply to chess.
In particular, you have condemned anyone who uses inductive thinking in this matter and yet what is that but a glaring example of inductive thinking, which is entirely inappropriate, as you yourself have pointed out?
I am bemused how you could think that is any sort of example of inductive thinking. It simply isn't.
In mathematics and related subjects there are theorems which start with a set of axioms and end with a proposition. They say that when the set of axioms is true, the proposition is true. I stated that chess satisfies a certain set of axioms defining a class of games, and thus all theorems that can be proven from those axioms are true about chess.
None of this involves induction: it is a very fundamental fact about deductive knowledge in general. It could itself be proven in a formal manner, as a theorem of mathematical logic.
What do you really mean by solving chess?
Are you trying to solve it like a puzzle, putting the pieces together?
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
Actually, if you refer to the second question, then chess will not be fun anymore.
If each side cancels out each other's moves, it will be a draw repeatedly like tic tac toe games.
Of course, it could also be a game in which one position is always guaranteed to win.