I think the chess example is not a very good one because part of playing chess skillfully is memorizing the board and remembering the exact moves that are made in the course of game to analyze it later on. If you rearrange the board at any point any chess player worth their salt will know.
That does not address the larger point that is basically impossible to know (for certain) that a given player or GM's decisions are informed by the expectations of the game without reading their mind. There's a certain level of truth to that, but for practical purposes I think it is largely irrelevant. Our actions and decision making process will always be shaped by what is expected of us, which behaviors are incentivized and the tools we have available. Such impacts tend to be felt over time. I have direct experience of this as a player and GM of indie games where people acted contrary to the spirit of the game. It took a couple of sessions but I have largely been able to suss such incidents out.
The other thing is that I almost always spend some time talking shop with the rest of my group. Those conversations tend to reveal a lot about the attitude players and GMs have towards the game.
I personally think there's a better reason why the chess analogy doesn't work.
The proposal is that the DM can make "whatever moves" could get them to the displayed new state, so long as none of them are illegal. But you don't take 7 turns in a row (or whatever) as a chess player. You alternate. And forcing white to move a piece
without knowing where the black pieces are would be awful--it would almost totally ruin the game experience. It doesn't particularly
matter that Black is assiduously making no moves that aren't illegal while the other player can't see.
And if you don't do that--if you only allow
one move at a time....then there's no difference between doing it openly and doing it secretly, other than the momentary surprise of "okay
which piece moved, now?" For anyone actually invested in playing chess, there would be no other difference.
The problem is, there just...isn't a game that can be used in this kind of analogy, to the best of my knowledge. The closest analogy I can think of, and it isn't a very good one, is playing
Battleship where one player is allowed to
move their ships after every round of the other person's actions, but only to locations that aren't blocked off, and only if that ship hasn't been hit yet. And I hope that this illustrates just how frustrating and un-fun it would be to do that!