It's hard, because he's redefined railroading as a personal definition, so it doesn't really align with how the rest of us use it. That may be where your confusion is coming from.
Yes, I'm idiosyncratic whereas you and others are universal and objective!
I think this is the closest thing I've seen to a thesis statement about what you think railroading is. But I think the jargon is holding it back here because many unrelated concepts fall into "control over the fiction". Consider:
1) The GM writes "captain Sparrow, large ship, +25% to base travel costs" before the game.
At that point, there is no shared fiction. There's just a note in a book.
2) The GM writes "pit trap, 10 ft deep, activated by 10lb weight".
Ditto, assuming that his is also written down before play.
3) the player says "I walk down the hallway tapping a 10 ft pole".
Now there's a shared fiction (I'm assuming the player is saying this in the course of play): the PC is walking down the hallway, tapping a pole.
4) the player says "I look for a ship captain in town. I want to find someone to hire for our journey.
Again, assuming the player is saying this in the course of play, there is a shard fiction: the PC is looking for a captain in town.
5) the player says "I try to trick the goblin into falling into the previously discovered pit trap".
This action declaration presupposes that there is a goblin, and a pit trap. But these are not normally parts of the player's "position" - they are not the PC, nor the PC's gear. What establishes that those other things are part of the shared fiction, and hence elements of the fictional position available for the player's action declaration.
Based on your previous responses, I suspect (1) is considered control over the fiction if it is decided during play, but perhaps not if before play. I suspect (2) is the same. I think you would not consider (3) nor (4) to be control over the fiction. But (5) would be, because the player learned that information already.
Personally I would consider actions like (3) and (4) to exert meaningful control over the fiction. But it seems like if the players can only take actions of this type, as in a fixed world sandbox, you consider this railroading.
Even if the GM writes down something about Jack Sparrow during play, it's not part of the shared fiction if it's just a thing written on a bit of paper.
(3) and (4) introduce new bits of fiction, but they represent the bare minimum that a player can do in a RPG - that is, declare what their PC is trying to do.
As I posted, I don't quite know what is going on in (5).
I think your thesis statement needs to be clarified by what exactly control over the fiction means.
The play of a RPG is all about the establishment, and ongoing generation of, a fiction. shared among the participants. It's this fact of
fiction that is one of the things that distinguishes RPGing from boardgaming, or purely mechanical wargaming.
The ongoing generation requires the fiction to be created. This is what RPG procedures do - and as I posted, in a pretty conventional/mainstream RPG, the two main modes of creation are (i) the GM narrating a new scene/situation/encounter, and (ii) the actions that the players declare for their PCs generate consequences.
How are these things done? Who establishes what the elements will be, what the themes will be, how they are related, what possibilities they open up or foreclose? These are some of the elements of
control.
If
all the players influence is what their PCs try to do, then as I said they have the bare minimum control that is consistent with the game being a typical RPG at all. But that doesn't have to be all. It's not all the players can do in Gygaxian dungeon crawling, for instance: when the players are in the process of obtaining information, it is the GM who is controlling the information; but when the players exploit that information to achieve their PC goals (in virtue of their knowledge of how their declared actions will resolve) they are able to exercise control. In effect, they are able to
oblige the GM to narrate the things that
they want to be part of the fiction (to give a very simple example: by saying "I lay a plank over the pit", and then "I walk over the plank", the player obliges the GM to narrate "You get to the other side" rather than "You fall down the pit").
The idea of
making a move that obliges someone else to make a particular move or at least
constrains their move space is a fairly standard part of game play. In chess, by checking the opponent's king, I constrict their move options. In bridge and similar games, by choosing what to lead I control the play of the cards, exploit my length in a suit, run those who are short-suited, etc.
In Gygaxian play, the players aspire to get to a level of knowledge of, and position in relation to, the fiction that they can similarly control it. (Which, in this context, isn't the same as narrating it. Just as I can control your play in bridge, without being the one who plays your cards.)
Burning Wheel uses a completely different set of techniques to also allow players to exercise control over the shared fiction.