I think you're still missing a point.
If the game to be solved is basic rules chess then the following algorithm secures a draw for White from the position shown and it's easy to prove that each the draw is secured whatever moves Black plays. This wouldn't however be regarded as a solution by most people involved in the thread.
White's algorithm: Move the rook to whichever of g8 or h8 is not occupied.
An ideal game under your definition could be
2n-1. Rh8 Kd2
2n. Rg8 Kd3
but in this particular position, if White follows the algorithm any game would necessarily be ideal game under your definition. It's easy to prove (I'll provide a proof if you insist) that each move in the above game is optimal for the player making it.
I would say the aim is rather to produce a game in which play by both sides is perfect as I defined it in #147 here https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=8 with proof that each move is optimal for the player making it.
Under competition rules your definition would be OK, but I think most people would understand OP's statement to be about the basic game.
I didn't actually say anything about repetition at all, but yes, it doesn't take proverbial rocket science to understand that any "solution" for a given chess position must discard repetitions after some set of criteria are met, or the analysis cannot proceed and runs forever.
Any entry level programmer that can hold down a job would understand this.
^ gibberish.