This has provoked me to a reply that may connect to some of what @Campbell has been saying about the "point" or "orientation" of play (my words, not his; and I'm still catching up so I'm conjecturing this connection rather than being certai of it).Dungeon choke points are not, IMO, railroading. Good dungeon design, especially for larger dungeons, usually requires some gating and separation of various areas. Sometimes that means there's a choke point. That says nothing about how the players should act, or how they can approach the dungeon as a whole.
Anyway: what is the point of the dungeon? And how does it interface with the mechanics?
If you're playing Moldvay Basic or AD&D then I don't think then notion of "railroad" really has much work to do. The risk in those games is of a boring dungeon, or one that is too easy or is a killer dungeon. Too many choke points could create these sorts of problems, but that would be very contextual. And I think it's generally taken to be reasonable in dungeon design to have soe levels (or sub-levels) which have only one entry/exit point.
But that sort of skilled-play/OSR FRPGing is not the only context in which dungeons can occur. In my BW game, the PCs explored a series of caverns chasing a dark elf. And later on have used the catacombs and sewers of Hardby to travel through that city without being noticed. Those situations are resolved through checks on Catacombs-wise, Perception, Speed etc. The existence of a choke point or a blocking wall or whatever is something to be narrated as a consequence of failure, not as a premise for or constraint upon initial action declarations.
I've run underdark exploratoin and travel in 4e in a similar fashion to what I've just described for BW. Eg it was a failed skill challenge that led to the narration of a PC falling through a very thin layer of stone into the river flowing beneath it. The thin stone wasn't a pre-given "trick" to be identified as a chalenge and then resolved: that OSR-style exploration-oriented-challenge-solving play is simply not part of the point of our 4e game. (And personally I don't think 4e is well-suited to it at all.)
Things would be different again in Cortex+ Heroic fantasy. Eg its fine in that system to estabish, as a scene distinction, No Way Forward or Narrow Choke Point or something similar. So like in classic D&D these things might easily figure as an aspect of framing. But mechanically they would operate like any other scene distinction and doesn't impose any distinctively strong restriction on permissible action declarations. Eg a player could delcare actions (based on, say, an approriate field of expertise like Outdoors and an appropriate power like Dwarven Senses) to (in mechanical terms) elminiate the No Way Forward distinction, which (in the fiction) would correlate to finding a way through or around. As that took place, and if it generated failures in the process, the GM would narrate those appropriately (eg imposing mental stress to reflect that the PC doesn't know where s/he is, or appropriate complications, or whatever).
TL;DR: we can't talk about whether some particular approach to prep and resolution (eg in this case the use of maps and notes having certain features) is railroading with a bigger sense of the context and orientation of play.
I don't agree with that last sentence because it posits two things as distinct which are intimately connected. "Adventure design", which in the context of dungeons and castles in a typical D&D campaign means maps and notes are tools used to frame situations and then to adjudicate action declarations. Eg the players say We walk 60' down the corridor and then the GM looks at the map and the accompanying notes to resolve that action.Sometimes the physical reality of a place limits options. Clever PCs might find a way around, and that's also a good thing too, but the place is the place. Walls have gates, so getting into the castle means that there will be limited options. In @Lanefan 's example above, where all entries are blocked except one is maybe extreme, but it's not a railroad. It could be a railroad, but I think that has more to do with how the DM handles player actions than it does the physical space.
<snip>
Generally speaking the whole idea of railroading centers on adjudication rather than adventure or encounter design.
If the point of play is (say) to have character-driven hijinks-ridden adventure, and if the unfolding fiction has delivered up entering a castle as the immediate focus of play, then the GM pre-determining the "physical reaity" of the place and hence pre-determining the outcomes of various feasible or even likely action declarations, that could absolutely be a railroad. And I'm not talking about this from a purely theoretical point of view. Castles and the like figure pretty prominently in a lot of my FRPGIng - especially Prince Valiant but not only that.
Eg in our Burning Wheel game when a pair of PCs wanted to enter the wizard's tower from the sewers and catacombs, I didn't refer to a pre-drawn map to determine whether or not that was possible. We resolved it via a Catacombs-wise check. When the check was failed the PCs still found their way in, but it took them much longer than they hoped which meant that their rival, whom they'd drugged, had recovered and was now racing them there: so in the end it was opposed Speed checks that counted. (The PCs lost, and so the rival got there first and murdered the NPC the PCs were hoping to rescue.)
I think a lot of discussion about D&D - especially when it comes to maps and notes - takes for granted that the skilled play/OSR-type paradgim is still operating. Which is fine, except if we look at the OP scenario that belongs to a completely different paradigm - that sort of burgomaster encounter isn't found in any of the classic dungeons that I know of - and the result is incoherence. The burgomaster encounter seems clearly to belong to some sort of "story" or "plot and drama" oriented RPGing - which of course is fine, except that maps-and-notes type adjudication is pretty ill-suited to that approach to playing the game.