I believe the contention focuses on the difference in how you play against an opponent. In chess, by this contention, ultimately what your opponent is doing has little bearing on what you do. There is a "correct" response to every board position.

Now, I think this is accurate for essentially single player sports. Golf and the like. Many competitive sports, however, you have to adjust what you are doing based on what your opponent is doing. Not just in a "correct" way, but to account for changing circumstances.

In the book How to Choose a Chess Move by Andrew Soltis, Andrew analyzed high level chess games and counted the number of moves into four categories. Here was the breakdown:

1. Forced moves 6% check with a forced move, forced defensive move, etc.

2. Book moves 28% opening moves following the opening book

3. Clearly best moves 30% there's one clearly best move out of all the moves on the board

4. Discretionary moves 36% there are many best moves, so one person would choose one move, but another person could choose a different move, and neither would be "right"

What does this mean for your playing?

It means that there is not always a best move, and so you shouldn't obsess over trying to find it. You have to accept discretionary moves.

This is what gives rise to chess playing styles.

I'm not really sure this disagrees with the assertion, though. Upwards of half of the moves are either "following a book" or "clearly best."

I'm also assuming for a large portion of the remaining "discretionary" moves, there is a "clearly bad" set of moves that should not be picked. This is a large set of things you have to memorize that are not really based on what or how the opponent will play.

Just because this correct response exists (and almost surely it's not unique anyway) doesn't mean it matters. What your opponent does and what his style is has huge meaning in practice and that will remain the case as we are not solving chess in near future and even if we did the solution will be too big to memorize anyway.

I think I agree. Just saying what my understanding of the assertion was. Basically, that there are only so many "meaningful" positions on the board. And at the upper levels, the question becomes more of how many of those positions have you memorized. Not, "how does your opponent play?"

As opposed to a game such as tennis. Where you really have to consider not just what you are capable of against a volley, but what your opponent will do with it.

No, chess is not about memorizing position and most games leave memorized territory fast. I don't know why this idea that chess is about memorizing openings got so much traction, it's nonsense. Top level games are rarely decided in the openings these days (although it happens that someone got nailed but usually it's because choosing very sharp variation and then forgetting the analysis) and there is a lot of play in positions never seen before in most of them.

Top level games are rarely decided in the openings because top level players typically don't make bad ones. :)

Is this akin to saying that top level tennis games are rarely decided by double faults. Likely true, but completely ignores the point that learning to serve over the net correctly is a vital skill. Just as learning a vast repertoire of studied moves and board continuations is key to chess.