This is at least a metaphor many sandbox GMs use. Where the Gm is like the program, but has greater adaptability because the GM is human. For most of us, at least for the time being, that is the thing that really separates the two mediums (a video game RPG is more locked in, has more preset material with interactions defined before hand----I am sure there are things like algorithms as well, but at the moment it still seems to lack the human GMs adaptability (though it certainly might beat the human GM in terms of being able to map out and track a world and its physics. A lot of the sandbox GMs I talk to, believe eventually programs will reach a point where they can function the same or better than a human GM. But I do think this is a lot closer to describing what is going on than discovering the GMs notes (still though, I think the obvious aim of an RPG sandbox is to create a believable world for the players to explore-----if you remove that from the equation with sandbox I think you are missing something key
I'll consider this progress. But if we can pull back the veil behind this metaphor, I think that we can work towards a better understanding of what's actually going on as part of this process. Again, I think that it's acceptable that your aspirational aim is the generation of a believable/living world, but the underlying crude and dirty
process by which GM and players achieve this is what is driving the conversation.
To supply a metaphor of my own: Your aim may be to give life to a beautiful garden; however, to create that garden, you know that you will be buying seeds, dirt, decorations, and tools and getting your hands dirty by hauling dirt/mulch, pulling out weeds, arranging plants, planting seeds, watering plants, trimming bushes, etc. How does one create a "living world" and what is the feedback loop interaction between player and GM, which can make facilitating such a world possible in a way that is distinct from games that operate with different feedback loops and play processes?
Now players may want to interact with a believable "living world" and the GM may want to provide said living world, but in order for players to do that in typical sandbox play, their actions have to be processed via the GM who often may set the difficulty, call or deny a check, or determine the potential range of outcomes for their actions. In order to engage the world, the players will be looking to the GM (and their rulings) as the GM exists as the intermediary between players and the presented fiction, because it's the GM's responsibility to procedurally generate the world. In order to engage the fiction that the GM presents, they have to engage the GM so that the GM can adjudicate their actions and hopefully generate additional fiction for the players to interact with.
I think that this is why it feels like "playing to discover what's in the GM's notes" for some, but it feels like it gets things wrong for others.
Party 1 sees "Player -> Living World (GM)"
Party 2 sees above as "Player -> GM -> World"
In other words, for players to interact with that living world, their actions have to get filtered through the GM's rulings/adjudications first. Full stop. In other styles/games of play, the GM is less of an "obstacle" per the rules. I do think that typical sandbox play implicitly recognizes this. IMHO, typical sandbox play, however, often tries to alleviate this through a number of ways: e.g., "neutral GMing," pre-built sandbox tools/subsystems, flexible generic system, play to find out what happens/let the dice fall as they may, etc.