I mean, it definitely helps. The production quality is insane. But the fact that the choices (or mistakes) have actual real impacts on the game going forward are as big as far as I'm concerned. I ended up with my hand being forced into combat early that made an encounter with a potential party member immediately hostile. That sucks, especially since I wasn't trying to do what happened in the earlier encounter. But in terms of a world feeling alive, having it actually react to what you do is pretty damn significant (unless "you're small and irrelevant" is intentional).
It's time developers come to grips with the fact that making choices matter is what makes it a successful game. I'm tired of storylines that don't make any sense except to give you a world to kill people in. Sorry folks, lore is important and that takes writers.
It definitely depends on the game, I'm perfectly happy with a game that has a story to tell, and tells it well. Not everything needs to have branching options and 50+ hour playtime. Some of the best stories I've played are short and railroady, WaW and BO1 campaing's are fantastically interesting and you don't make a single choice in them.
I would say if it is all about the gameplay, like Serious Sam or Doom, then the story doesn't need to be that important and dexisions don't need to matter. But if the story is front and center, like Baldur's Gate and most similar RPGs, the story and how choices impact the story need to be well done so it doesn't feel on rails and replaying it is enjoyable.
I don't think the lack of choices is necessarily a bad thing. The original Doom had no story choices (it barely even had a story) and it's still pretty good even by today's standards. Half-Life 1 and 2 pretty much had no story choices as well (there was 1 at the end of the first game) and the first one in particular is considered revolutionizing how stories are presented in games.
What I do think is an issue is when the game presents you with a choice that doesn't matter. Bioshock Infinite is the first that comes to mind as the game puts quite a few options front and center, but really none of them matter (except the very last one) and the game even implies that the choices deliberately don't matter because "constants and variables". Thus those choices, at least for me, detracted from the story because there was never no need to make me make a choice.
In that sense I agree that choices should matter, but I think a better wording is that if you're going to have choices make them matter or don't have choices in the first place.
It gets super confusing when you do stuff in the wrong order though. Missing a clue because you didn't read the right book or something but then randomly finding the end of the quest and everyone is talking like we know all about it.
Usually it recognizes it. Sometimes it doesn't though. I'd hope those instances get patches eventually. Even worse though is when something triggers for something you didn't even do. I've had a party member get angry at me for something that I did the opposite of. It's a pretty solid game, but it's not totally bug free, which is expected with so much complexity. Who knows, it could have just been a cosmic ray that flipped a bit and not even their fault (though I doubt it).
I doubt that they're referring to Minthara; you have to make an intentional series of decisions to >!murder a bunch of people!< in order to get her in your party. It's relatively easy to miss several origin companions if you're not the type that explores the whole map. And one of the origin characters starts with >!a quest to kill one of the others!<.