Duff, cool guy that he is, was reading my last few posts and sent me another video to watch on the subject (or a subject that's incredibly tightly related). I highly recommend a watch, MrBtongue makes some really good points. The phrase I use, "Player Agency," is more of a tabletop roleplaying concept -- the idea that players get to make decisions and perform their own actions, as opposed to "railroading," where the player is "on a track" to just experience the story as the Gamemaster has laid out. MrBtongue uses the term "Choice and Consequence," which is a very video game expression of the same sort of concept: the player makes choices which have consequences in the narrative. He specifically notes that there are two forms of this "choice and consequence" theory. It can be used as a form of simulation: "How does the world realistically respond to the actions of the character," which helps reinforce suspension of disbelief and makes the player consider their actions more carefully, factors which should be desired in any role-playing game. It can also be used as a transparent ploy for replayability, which he regards as a more negative aspect. The player's choices really don't change anything except for branching the storyline, often in non-intuitive ways. Finally, MrBtongue's guide on how to do choice and consequences the right way at the end of the video is absolutely worth a person's time.
I don't entirely agree that choice/consequence systems that emphasize replayability are always bad things. I will agree that the choices which do nothing but branch the storyline in a way that doesn't really relate the choice at hand are, well, "non-optimal," to put it nicely. Situations like the one MrBtongue mentions in Mass Effect 2, where doing a character's loyalty mission is the difference between the character meaninglessly dying in a cutscene at the end of the game from a stray bullet are very silly. That's pretty much just a way to pad game length, call it a choice, and get another bulletpoint on the back of your game box. I guess I could say I'm in support of the "type two" or "replayability" choices when they can at least masquerade as "simulation" choices. Think about the difference between Open Palm and Closed Fist in Jade Empire. In a way, that morality system is mostly one about replayability, but it also affects how your character acts and is perceived by the world. It's a way to add replayability while appearing to be a simulation. It changes events in an intuitve manner, rather than a non-intuitive or unrelated way. I'm also a little more generous as to the idea that a choice which is really just a character choice, one that affects the way your character perceives or acts within the world is a good choice, not just a choice that affects how the world perceives or acts around your character. In the hands of an adept storyteller or developer, that difference may mostly be a matter of semantics (is the world a little darker, or does the character merely perceive the darkness in the world more starkly, for instance).
Another point that MrBtongue brings up is that consequences are much more powerful (and in fact, are only powerful at all) when they affect a character that the player cares about. In Fable 2, there's a scene where the player is given the choice between having their character be aged to an old age (visually; this consquence has no bearing on game mechanics and apart from any visual attachment you have to the character, it is completely meaningless), or "tricking" an NPC generated solely for this scene into having their youth stolen instead (this is, of course, the "evil" option). Shamus Young talks about how, when confronted with this choice, he didn't even feel a pang of guilt into making the peasant woman NPC be aged. That consequence affected an NPC who you've never seen before and will never see again, which reduced its impact on the player to near nothingness. The only meaningful effects of that change were "do you want to look old, or have your evil-number get bigger?" In other words, this choice has effectively no consequences (due to Fable's mechanics, it's not terribly difficult to mitigate morality effects, at least in the Fable games I've played, which, granted, do not include the second, as it was never ported to a game system I owned). Fable does feature at least a little focus on allowing the player to customize their character's appearance, so there could, depending on the player, be a consequence to growing old, but that's hardly a compelling consequence that affects either replayability or how the world treats the player. It is neither a simulation, nor does it increase replayability. (Technically it's a "simulation" choice, since the morality system affects how NPCs treat the PC, but as I mentioned before, this is easy to mitigate and so is effectively meaningless.) There is a rule in tabletop playing which not every GM lives by, but the good ones do: don't make the player roll dice unless failure is interesting. Similarly, it's not a great idea to give a player a choice that doesn't matter in a video game. A player quickly loses faith in a narrative that gives them choices, and then disregards those choices. I've almost beat The Bureau: XCOM Declassified, but the way the game simply disregards every choice that I've made has caused it to be something of a chore to play. When you chose the "let's not kill all the humans" option, and then everybody acts as though you picked "hey, let's kill all the humans," you start to wonder if the game developers intended to actually let you choose anything.
Like MrBtongue points out, you don't need choice and consequences for every narrative. It can be enough, especially for non-RPG genres, to just give the player a good experience. A player doesn't need to always make choices. A player might be disappointed if they don't have player agency, but it's better to just flat out not have player agency than it is to pretend you have player agency and then not actually have any player agency. Then the player feels betrayed by the game and the narrative. "Hey, I turned that guy good! Why is he now suddenly evil for no reason?!" "Hey, I just said that we would find a peaceful way out of this, why are we arming the nukes?" Disregarding the player's choices is a worse sin than never giving the player any choice at all, because then at least the developer and the player are on the same page of the narrative. Once you betray the player's choice (at least if you do so without a really good reason), you've done a lot of damage to the player's trust in the narrative and, as a result, broken the player's suspension of disbelief. The player's trust in the game and the game's narrative can be a very difficult thing to win back, so unless there's a very good reason, it's not going to be worth disregarding the player's choices just for the sake of them being able to make choices in the game. Skip the bullet point and just make the narrative stronger. A player is much more likely to replay a game because it had a great, really solid narrative experience, even if they didn't make any meaningful choices, than they are to replay a game that had a bunch of choices for them to make which are ultimately meaningless or ignored by the game's narrative structure.