By "the fiction matters to resolution" I mean the difference between a game whose moves refer to a shared fiction, and one that doesn't. RPGs are examples of the first; chess and other boardgames are examples of the second.
I've seen people try and construct counterexamples like blindfold chess. But blindfold chess doesn't use a shared fiction. It is - in its core process - no different from solving an arithmetic problem in one's head rather than on paper. It requires memory (perhaps aided by visual imagination) but the resolution process is still a type of deterministic logic/geometry. Resolution is not by way of imaginative extrapolation of a fictional state of affairs.
This is also why I regard comments such as you can roleplay while playing Monopoly, for instance by (in imagination) tooting your horn and waving to the passers-by as your motor car playing piece passes Go, as missing the point. Key to RPGing is not that we imaginatively say stuff but that the stuff that we imaginatively say actually matters to how the game unfolds. That is not true of Monopoly, no matter how vigorous the play-acting; whereas it is true of a Gygaxian dungeon-crawl, no matter how pawn stance the players' orientation towards their "pieces" (ie their PCs). For instance, there is no rule in classic D&D that tells us (for instance) that an axe might be used to break through a door. There is no axe piece, no door piece, and no rule connecting them - which contrasts, for instance, with the rule in the Talisman boardgame about using an axe to build a raft. The reason that an axe can be used to break through a door is because of a table consensus that that makes sense as a possibility in the shared fiction.
RPGs also have fictional position. That's an expansive notion, but at least as I understand it, it includes such elements of play as that my PC is standing at a barred door, holding an axe, which is not about the state of a token on a board (real or imagined), but rather an assertion that everyone at the table agrees with, but in a fictional rather than doxastic mode. The fictional position makes moves possible not because of geometrical or similar logical/deductive relationships (cf blindfold chess) but because we can, collectively, imagine what a person standing in front of a barred door and holding an axe might do.
I think two things are being run together here. There could be - and, presumably, are - texts to support freeform RPG. And a non-freeform RPG can be played without a prior text, if the rules are negotiated and agreed in the course of play by the participants.
All a rules text is is a reduction, to writing, of the procedures and/or rules of play. Those procedures and rules "exist" (I use scare quotes to sidestep the metaphysical questions about the nature of rules) even if not reduced to writing; and freeform has procedures (if not rules in the strictest sense) that could in principle be reduced to writing, even if often they're not.
Game texts are prescriptive because they contain rules; and it is the general nature/function of rules to prescribe.
RPG rules generally prescribe ways for a group to come to agreement on the content of a shared fiction, in a play context where it is implicit and perhaps explicit that no single person has unilateral authority over the whole of the shared fiction as such.
It's no mystery that rules can set out methods for how to establish a shared fiction without stating what that fiction should be. Similarly, a book of instructions on how to build a house safely and legally will be prescriptive without telling you what sort of house you should build. When I was a kid, I had a book that told me how to program in simple BASIC without telling me what I should program (one of the things I remember programming was a simple PC generator for Moldvay Basic). Etc.
I don't really follow this. When I read (for instance) the rules for building a PC in Moldvay Basic, I don't feel the meaning of the text as something inspired by the text translated through my performance. Rather, I read the rules and follow the procedure, much like following a recipe. And then, when I play, I establish fictional position, and resolve actions declared on the basis of that fictional position, by reference to the rules.
If the sorts of texts you are meaning are campaign guides, scenario outlines etc I still don't really follow. When my group uses, for instance, the Greyhawk maps to establish some bit of fictional position, or to reach consensus on the resolution of an action (eg We travel from the Wizard's Tower to the Forgotten Temple Complex - ie from a point on the southern Bluff Hills to a point nestled between the Troll Fens to the south and a spur of the Griff Mountains to the north), we look at the map, incorporate that into our shared imagining, and go on by straightforward extrapolation.
You've largely lost me here.
Some game texts are constructed subsequent to play - this is true of the original D&D rulebooks, and also of the GH Folio. Some may be constructed prior to play, although if they've not been tested at all we might expect them to be weak - I have certainly written house rules on the basis of imagination and prior experience alone, without testing them, and so those bits of text have been constructed prior to any play using them. Not all of those house rules have been failures, either, although some have been.
Anyway, it seems to me that you are treating as somewhat difficult or mysterious the possibilities that rules can be authored to govern the creation of fictions, without thereby dictating the content of those fictions and that fictions authored by one person can be incorporated by others, in whole or in part, into their different fictions - whereas I think both possibilities are quite straightforward. The first possibility is just a special case of the general phenomenon of an instruction manual for some activity that is not fully prescriptive as to the end product (what sort of house will I build, now that I know how to build houses? how many layers will I put on my cake, now that I know how to bake cakes and spread cream and jam between layers? etc). And the second possibility is just a special case of the general phenomena of (i) language being public and iterable, and (ii) assertions in non-doxastic modes, including fictional modes, being a thing that is pretty innate to humans.
