You're correct, in that given a board state the right move can always be exhaustively computed, because the game has no randomness or hidden information. But enough computing power doesn't exist on the planet to iterate through all the possible states.

The word you're looking for is "deterministic", rather than solved. Solved is usually used to mean the exhaustive computation has been done. Deterministic would mean it could be if enough computing power existed, but for chess it doesn't.