So what is a sandbox game anyway?

[OldTrees1]

I'd say it's wrong to view / approach it as a matter of power and dominance in the first place.

All human relationships based on power are, IMO, halfway to toxic just by being about power.

I can see the faulty communication just got worse. Any objections you have to the field of game theory are better pursued separate from your views about relationships. If that sentence seemed like a non sequitur, then consider how your statements appear.

So, starting again, trying to give you the context you need to understand the dialogue you butted into:

1. In a game with a DM, the DM presents the PCs with a choice.
2. (reserved for later)
3. The Players have their PCs make a choice.
4. The DM then decides what will happen.

In step 4 the DM has the capability to exercise their ability to decide what will happen in a manner that negates the relevance of steps 1 and 3 by deciding what will happen without regard for the choice the PCs made.

Do you agree that the above capability does exist even if we both frequently criticize it? (congrats you understand the first post)

Now watch as the DM does 1 extra thing and the consequences thereof:

1. In a game with a DM, the DM presents the PCs with a choice.
2. The DM decides to have the PC's choice determine what will happen no matter what.
3. The Players have their PCs make a choice.
4. The DM then enacts what the PC's choice determined will happen.

Can you see how the addition of step 2 changed the nature of step 4? If step 2 exists then the DM does not have the capability to negate steps 1 and 3 because the DM intentionally sacrificed that capability in order to make the choice in 1 & 3 a meaningful choice.

Do you agree that such meaningful choices exist and are not illusions? (congrats you understand the second post)

Edit:
After this post Windstruck made a 3rd post that repeated the content of the 1st post. Namely that prima facie, the DM is the final arbiter of what happens.

Did that help clear things up for you about the dialogue to jumped into? It was not about calling DMs Doms or about advocating or approaching either as being about power/abuse. Rather it is taking the lessons of game theory and applying them rigorously to see the primitive components of the multiple person interaction that leads to the difference between the illusion of choice vs the reality of choice in a discussion about whether choices can be real (spoiler: they can).