This goes back to my question: what is the job of the players?
Isn't that kind of up to them? Presumably, they entered into some kind of negotiation with the burgomaster for a reason. For the scene in question, achieving the result they wanted from the burgomaster would be their current job.
Is guessing/inferring what the GM has decided will be the realistic response of the tyrant, or the guards, a meanngful choice? It might be meaningful inference, but if the inference is performed successfully then where is the scope for choice?
Depends on what they're negotiating for. They have a pretty broad set of choices in front of them that
don't involve 1) insulting him, 2) trying to take him hostage - either of which should have had fairly predictable negative results (particularly the second).
Another way of thinking about "meaningful choice" is this: do I go along with the tyrant, or do I scornfully throw his offer back in his face? That's a choice about what sort of person I (as my PC) want to be, and what sorts of things I want to do. And if I choose to be the sort of person who scornfully throws the tyrant's offer back in his face, should it follow without further chance for action declaration that my PC is dead?
Since the OP made no implication that the PC would be dead with no further chance for action declaration - that's pretty much a non-starter as an argument. But of course a player could choose to play a PC who throws the tyrant's offer back in his face scornfully - but should he not expect to suffer the predictable consequences? Or should those consequences be unrelated to the established nature of the tyrant or not based on the scornful rejection? If they are, then what's the point of knowing anything or even trying to make rational choices?
Of course, a player could choose to play their PCs in a non-scornful manner or at least intelligent enough to swallow the scorn and turn down the tyrant's offer in a more deferential manner and then take his frustrations out on something else later once the negotiations have been peacefully completed, even if not successfully.
Should the game be a puzzle? A game of following others' leads? A chance to express the personality of one's PC? These are real questions.
In most cases, I would figure it's a mixture - there will be puzzles such as how to topple/defeat Strahd (at least in the short term), there will be chances to express the PC's personality, and there will be times when making an ill-considered choice should have negative consequences.
As for the role of the dice - I think of them as a way of randomising outcomes. Roughly speaking: the players want their PCs to succeed; it's the GM's job to establish opposition or adversity; the dice roll tells us, on any given occasion, which it is. That's pretty much been their role since D&D was invented. I don't understand why you would denigrate the use of dice in the way that you do.
Sure, but another aspect of D&D is the possibility of skilled play - and that sometimes means the players making choices that indicate their PC's actually understand the world around them and experience it as though it were real to them with real cause and effect and consequences for the things they do.
Although you refer to the PCs I think you mean the players. The PCs are making guesses only in imagination. The players are actually deciding what moves to make as they play the game.
That's really a pointlessly pedantic nitpick since you knew exactly what I meant.
And you seem to be assumng that it is the job of the players to guess, or to infer, what it is the GM has in mind. That's one way of playing the game. I don't quite see why you would describe the resulting choices made as meaningful. Putting the right number in the sudoku box is a choice, but it's a meaningful one only insofar as if I do it wrong I won't solve the puzzle. Is RPGing puzzle-solving?
I don't assume it's a question of inferring what the DM is thinking. A meaningful choice is one that is taken with a reasonable understanding of the expected consequences - consequences that will be distinct from the ones you'd face if you made a significantly different choice. If the outcome isn't related to the choice being made, like the thin-skinned tyrant just laughing it off when insulted or the guards were too drunk to make an arrest, what kind of meaning would it have? None, it's just a thing that happened, and not really a result of a player's choice.
