To what extent is a player expected to play a boring game? "Boring" is a word that covers a wide range of possibilities.
For instance, if I sit down to play a game of five hundred or bridge, I have to expect to sit and observe whle others play their cards. But (in my view) someone who takes 5 minutes to decided on their play in a casual game of cards is being pretty discourteous! I've plenty of times been in situations where other players - in a card game, a board game, or similar - urge a very slow player to speed things up because it's not fair on everyone else.
That's not unreasonable, though as with TRPGs it might depend on table culture, things like how chatty the players are, how well they know the game, the extent to which the game is an excuse to socialize. Some players just play more slowly than others, too. In a competitive game, there might be some gamesmanship involved in pacing your play, as well, though how acceptable that is seems like a table convention (probably not formal enough to be a rule).
In the context of a RPG, what power does a player have to speed things up or make things not boring?
{snip}
It's a long time since I played (as opposed to GMed) a D&D campaign. In that campaign much of the action involved the GM dealing with one particular player (whose PC was the prophesied one, naturally). The rest of us entertained ourselves by establishing a pretty fun intraparty dynamic, set of subsests, our own theories about the meaning of the various prophetic texts, etc. The GM largely ignored all this stuff and - in the end - ended up "blowing up" the campaign world and thus invalidating all the fiction the rest of the players had created by teleporting the PCs 100 years into the future. As a result the campaign ended shortly after when I and others quit.
As I said, boring covers a wide range of experiences and in the context of a RPG can reflect a wide range of ways that the game is ending up. But I don't really see that a player is olbiged to sit through a tedious scene where nothing is progressing and the fiction is not moving forward. Was the OP describing such a scene? I dont know; I wasn't there. Some of the posts others have made about this module make me think that's a possibility.
So, that DM was clearly a bad DM. I don't get the feeling the OP is. Should you stick in a campaign that is as stifling as you describe? Probably not. Should you allow your fellow players to finish a scene, even if you think it's maybe running a little long? Probably--if there's a pacing problem, or if the campaign is focusing too much on an aspect of the game you don't enjoy, you should take it up with the GM (and maybe your fellow players), before crapping on their fun. Courtesy is a form of thoughtfulness; the player's discourtesy is why I described this play as "thoughtless" above.
What has been "telegraphed" about this NPC? That he's mad and angry? That he wants to see the PCs (or perhaps that the PCs "have" to meet with him because that's what the module says)? What expectations are the players meant to have? What are they supposed to be doing in the scene? Listening to the GM? Going along with the mad NPC? Is any back-and-forth expected, and if so about what?
Per the OP:
Going into the meeting, they knew the ruler was unstable and severely punished any dissent in his land - having heard from various NPCs and seeing it firsthand.
I do not know the adventure any better than you do. Nor do I know how the OP went about conveying that to the PCs. I don't know what the intent of the PCs who were negotiating was. The OP says it was going pretty well--which implies progress was happening, at least in some direction--before the "probably bored" player started insulting the ruler. I don't see anything about "severely punished dissent" that implies "tolerates being insulted." Frankly, he sounds as though he's the sort of weak ruler who'd overreact to any little thing--and even if being insulted is a little thing, being physically assaulted is not.
Which also relates to the suspension of disbelief. Where is it established that the Mad Tyrant would execute anyone who insults him? In the GM's mind? As a result of reading the module? This looks like what
@Manbearcat has called "GM setting solitaire play".
I think that a GM who sticks to
an image formed in his/her mind - whether via his/her own invention or from reading the module - and then uses that to inflict "realistic" consequences - wher the realism is only in his/her mind - is likely to run into trouble as soon as the players try and play their own preferences or conceptions of the fiction.
Maybe the OP misunderstood the adventure; maybe not. I don't get the feeling the OP was invested in the setting in the way "setting solitaire play" implies.
As to the GM sticking to an image formed in his mind ... isn't that a big part of what the GM is supposed to do, at least in a game like D&D? Isn't the DM supposed to have the scene in his mind and convey that to the players? Isn't the DM supposed to have the NPCs in his head and convey those to the players, and have them react to the PCs according to their natures (shaped by whatever mechanics come into play)? If the players don't understand something, that's on the DM, sure, but I don't see why trying to have the world behave at least plausibly is going to interfere with the players playing their characters, following and eventually achieving their goals.
That's why I've said that it was the GM, not the players, who resorted to violence. And why I think the idea that the players should have just had their PCs surrender is unrealistic. In practice, surrendering is thorwing themselvs on the mercy of the GM. Where do they get the information about what the result of that will be? How are they meant to know what the GM thinks is a "realistic" consequence of surrendering as opposed to fighting?
I'm not sure having a character behave according to his nature can fairly be described as "resorting to violence."
Yes, getting players to surrender is hard. The player who attacked the ruler when he called for the guards at least wasn't behaving unreasonably, and it sounds as though there were some interesting and tense moments as the other two players talked their way out of the ruler's chambers. And the king's guards didn't kill anyone in that moment--that wouldn't have been an execution. There were two players looking at execution, and two that weren't.
I guess it seems to me as though you're willing to throw the GM under the bus, here, while I figure the players (or at least one specific player) to be more the problem, in this specific instance; and that the problem is probably more among the players than between the players and the GM.