Bedrockgames
I post in the voice of Christopher Walken
This is complicated by your limited understanding of how a GM can control players, but your intention in the above is I think good even if your strict definition isn't. Let's call it railroading when the GM wants to control what the players can accomplish or how they can accomplish it, and I think we'll both be in agreement.
I am trying not to be insulted by this phrasing

I would honestly need to think about this definition. I think the real genuine definition of a railroad is the GM taking hard measures to keep a game on the course he has set. Merely wanting to control might not quite rise to railroading if the GM is allowing that control to slip. When people say railroad what they mean is the players can't get off the aventure or story path the GM has set no matter what they do: the GM is fixing the game to go in the direction he wants it to go. So the GM doing things like fudging, moving prepped material around so it is always encountered, even if they go in the direction where it wasn't initially placed, etc.
Not just simplistically. I think this is absolutely giving the players agency. It is definitely not railroading (a railroad would be blocking the party from the bootlegging endeavor through various means until they return to the manual quest the GM has in mind).Simplistically you might think that the party that chooses to start a bootlegging enterprise in Dee instead of helping the guy obtain the Manual of the Nine Claws has more agency and if the GM says "yes" that they are letting the players go where they want to go and set the agenda.
Again no one is disputing that the GM makes things happen. But he didn't make the idea for bootlegging happen. That is something the players introduced. Like I said before, I think you are taking the phrasing the poster used overly literally and to listening to what they were trying to say. They were talking about a style of GMing that is reactive to the agendas and actions the players set and take. That doesn't mean the GM stops making things happen in the settingAnd most of the time you would probably be right, but in both cases the GM is equally "making things happen".
This can be a bit of a side trek, but lets say I have envisioned this interesting story in which this guy obtaining the Manual of the Nine Claws is one step, and my players don't cooperate but decide to set their own agenda and become bootleggers. Bootlegging isn't an inherently interesting occupation. It's mostly going to be tedium with long periods establishing yourself as trustworthy business men in the black market, finding buyers, earning their respect, and basically living out a pretty normal life like going into work every day and managing finances.
But the point of the style the poster is talking about is to let the players go there and see what happens. Bootlegging is potentially filled with conflict, competition, outright wars for territory, so it need not be dull at all
So who is the railroader? The one that gives the players a realistic but boring campaign as bootleggers, or one that "makes things happen" by upon seeing that the players are excited about this theme goes ahead and begins introducing dramatic twists, foils, rivals, and interesting story lines around the player's choice? Which group of players ends up with more agency? The one that is given a realistic but boring story where nothing exciting happens, or the one where the GM is introducing plots and devices of his own imagining? The notion the players that are creating the boot legging story are creating all their own fun is a flawed one. It's not real. It's an illusion.
This is a false choice. If the issue is you don't want the game to be boring, then don't make bootlegging boring. No one is saying they are creating the story. But the GM is also not creating the story. The GM is allowing the players to do what they want. The GM had an adventure planned about a manual, but the players didn't go there, so now the game is about bootlegging. That is agency. The story is emerging as a back and forth between what the players decide to do and how the GM and system react. But I would be reluctant to use language like story here. It is an evolving situation
Yes, but you do that by making things happen. That's why I said every good GM utilizes the coincidence. Wherever the players go, there is the fun. Real life doesn't work that way. It's an aesthetic choice and you create it as a GM by making things happen.
Again, no one is saying the GM doesn't make things happen. The point is: it isn't soley the GM deciding where things go. The players have freedom to do what they want, to go where they want and the GM is expected to keep up using a variety of means. Whether the GM is utilizing things like dramatic coincidence, that will be very dependent on the kind of game the GM is running. A lot of Gms who play this way will avoid that stuff, many will be using tables, NPCs motivations, group motivations, setting details as their guideposts for what happens (and the players are always free to interfere with that however they wish and to steer things in other directions). It is an organic process.
There is a spectrum here, but it's a little more complicated that most people realize when they are for "team sandbox" or whatever. There is a difference between linear and open world games in presentation and feel, but we can't easily say which is better or which has more agency or that one doesn't involve the GM making things happen.
To be clear here, I am not knocking linear adventures. I am just defending the idea that a GM who says "I let the players decide" is genuinely trying to let the players have agency. I run a range of games. Sometimes I run what I call a dramatic sandbox. Sometimes I run investigative adventures or dungeon crawls. Sometimes I run monster of the week. I also will occasionally blend these approaches together. It depends very much on what I am running and why. I also played a ton of adventure path* and loved it. One frustration I had with gaming, especially my D&D gaming, in the early 2000s, was I never felt surprised enough as a GM (so that is why I explored other approaches like sandbox)
I will say this though. If you are running open world, in my opinion, both as GM and player, you are giving the players more freedom, and I would equate that with more agency. However you could argue that isn't always a good thing. You may be giving them too much freedom and not enough focus and would be happier if you constrained the freedom to operating more within a planned adventure. I am not saying sandbox is the best style (I am not even fully advocating for sandbox here). Sandbox in fact can be a pain in the ass if you aren't enjoying yourself. When I do run sandbox type games it is usually because I want a low prep, let's see where the players go, kind of thing. But sometimes I want a proper adventure with structure to it. When I do the later, there is less agency overall (I mean they can up and leave the adventure but that brings the session to a halt). But there isn't no agency, and there isn't less fun. For example I just ran this investigating adventure during Halloween. I didn't feel like running a sandbox. I wanted a proper halloween adventure. After that I ran this monster hunt that October, then this dungeon crawl to cap off the month. I think people should run whatever works for them. And I think it is a mistake to be a servant to some ideal about 'sandbox' or 'agency' that leads to a game you aren't excited about or have trouble running (generally I am wary of pure sandbox play because I think you do need to have exciting things happening to keep the game fun: but that is just my style).
*using this term loosely to just refer to that old structure of adventures built around EL/CR in the 2000s.
And remember, I start with a session zero where I get player agreement as to what sort of game we are going to play. So if suddenly in the middle of that, someone wants to change what the game is about and get off the adventure path and become a bootlegger, something probably went wrong. If I'm such a bad GM that I can't make the adventure path fun and now everyone wants to get off the train, then chances are I can't make bootlegging fun either.
That is totally fair. I am not telling you what you ought to do at the table. And I think if you are having a session zero you are honoring the agency of the players. And also to be abundantly clear I am not saying adventure paths make you a bad GM. If you and your players like that structure, then that is what you should run