I am not seeing that in your answers. And 40 years ago people didn't talk about how to run sandbox FRPGs Because while sandbox campaigns were being run there was no sense they were something different than RPG campaigns in general.
I didn't say they used the word "sandbox". But they talked about the things you and
@Bedrockgames talked about: GM creation of setting, the players declaring actions that move their PCs through the setting, GM as neutral arbiter of actions. Discussion of this can be found in White Dwarf - Lewis Pulsipher in relation to D&D, other contributors in relation to Traveller; to a reasonable extent in Gygax's DMG; and tools for doing it, such as random events charts, are found in various places including the original OA. Campaign Law for Rolemaster also presents world-building as oriented towards a sandbox approach to play.
I remember having conversations about RPG world-building with a friend who was also a serious humanities/social science student (we are now both academics in our fields) over 30 years ago. I still have notes about NPCs, factions, places and possible events that I made back then.
The contrast between arena-type play, dungeon-of-the-week type play, GM storytelling, and "open world" exploration-type play was plainly evident in the RPG club I was a member of in the early 1990s. I can't recall now if we had a neutral vocabulary that we used to talk about it - given the preferences I and my friends shared, we talked about serious vs non-serious play, and railroads. Serious play involved rich settings with backstory that was relevant to and manifest in the current play, and relatively richly-realised characters. The approach was a sometimes unstable combination of, or alternation between, purist-for-system simulationism against a backdrop of GM authorship of setting, and vanilla narrativism.
That post doesn't say anything about Burning Wheel, Apolcalypse World or similar RPGs.
During an RPG campaign, the group could take the narrative, story, and other literary concepts into account. What if you didn't?
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The alternative thesis that I developed in the course of running sandbox campaigns sidesteps the issue of literary terms for RPGs. Along with whether anybody participating is collaborating on a story.
The play of Burning Wheel or Apocalypse World doesn't use or rely on literary concepts such as "narrative" and "story". They do not involve anyone collaborating on a story. In fact the whole point of the design is that no one needs to collaborate on a story or use literary concepts such as "narrative" or "story".
What if instead, it is treated as a pen & paper virtual reality that one visits as some imagined character having adventures? Run with pen, paper, dice, and with a human referee adjudicating.
This is a very general description. I don't see how it doesn't apply to BW and AW.
The outcome is uncertain but the players know with good planning and some luck what they want to do could be done even if it is as ambitious as conquering a kingdom or toppling an empire. Or something more modest such as protecting a neighborhood in the City-State of the Invincible Overlord.
This is also very general.
A game of AW could involve protecting the hardhold. A game of BW could involve conquering a kingdom.
the essential steps are the group choosing the setting that the campaign will focus on.
This is a key step in starting the play of BW or AW.
Preparation for the "visit" for both the referee (campaign prep) and players (character generation). Then the "visit" begins when the campaign starts.
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Like a real-world trip, the group and players may have a bunch of goals they want to achieve.
The referee's job is to be a neutral arbiter adjudicating what the players do as their characters and bringing the setting to life. Along with fleshing things out as a result of the players' choices as make their way through the setting. The players are free to do anything their character can do within the setting using whatever knowledge they have about the setting.
As I already posted, these passages are where one can find the difference.
Both BW and AW involve players formulating goals for their PCs. But the GM is not a neutral arbiter. The GM's decision-making, as guided by the action resolution rules, is expected to have regard to the goals the players have adopted for their PCs.