I think another feature, which is brought out in your example, is that the default starting point for a certain sort of sandbox is
low stakes player decision-making. Play begins with the players in a position where they need to acquire information, and they do that by making low stakes action declarations that will prompt the GM to reveal that information.
In Gygax's PHB advice on Successful Adventures, he draw an express contrast between player goals of
obtaining information, and - once that information is obtained - the different, and higher stakes goal, of
acquiring a particular loot, perhaps by targeting a particular dungeon denizen.
Here's a scenario that also starts in a room, with decisions to be made - but they're not low-stakes!
Burning Wheel The Sword Demo Adventure PDF
When players sit down with me to play this demo, I give them the following preamble:
You’ve journeyed long through this crumbling, ancient citadel, down through ruined chambers into muck-filled tubes. You arrive, at last, in the wreckage of this collapsed temple. Laying on the shattered altar, in the chamber before you, is that which you seek: The sword!
After the preamble, I lay out the characters and describe each one in brief. After the players have chosen their characters, I instruct them to read their Beliefs. Then I simply ask, “Who gets the sword?”
Mayhem ensues, and suddenly we’ve got game. . . .
I’ve found it useful to start the scene with the whole group in the doorway to the chamber - still in the tunnel, really. The Roden, if he’s in play, should always be in the lead.
Here are some of the Beliefs:
The Dwarven adventurer: This sword was a treasure of my clan for generations, stolen by foul Roden and abandoned here. I’ll restore it to its rightful place among my people.
The Elven bard: This sword was made by my father. Using its markings, I will demonstrate its origin to my companions so they cannot dispute its ownership.
The human gambler: Master Kogan of the gambling house is going to break my knees if I don’t pay off my debts. I’ve got to get paid in this venture! and also I was the one who figured out where this treasure was; it belongs to me!
The Roden cultist: To enter the Fields of Paradise, I must present my Visionary with this fabled sword.
These players have options as to which path to follow. They can cooperate, argue, fight, try to betray one another, etc. But I don't think it has the character of a sandbox.