A lot of games have the DM be just a player. It is also a popular game play style.
I've never seen
anything like what you describe. I have never
heard of it from anyone but you. I have spent pushing 20 years frequenting various forums, talking with friends, and delving into the TTRPG space. You, and
only you, have brought this idea of the "player-DM" who sits there quietly doing nothing but nodding at the players' declarations.
I strongly suggest that, given the sheer number of people who are reacting incredulously at your descriptions, you reconsider whether this style is
actually common, or is perhaps either specific only to your general gaming sphere, or a misunderstanding on your part.
The problem I have is this sounds like a normal game.
I assure you, it is not. It is one style. There are others. I wouldn't enjoy playing a game with the specific kinds of stuff that most sandbox games do, because I'm not good with that particular kind of thing. I suffer analysis paralysis when given
that kind of creative freedom; I call it the tyranny of the empty page. I am quite good with only very very minor constraints, but give me
total freedom and my brain shuts down. It's like...if I have a hundred options, I can filter them and pick one that is best by whatever metric seems reasonable. But when I have
nearly infinite options? My proverbial filter clogs and nothing gets through.
(This, incidentally, is one small part of why I like PbtA-type games. They have the player-driven experience, but in a way that drives the players to respond to
this current situation right at this very moment, which is enough to jump past my analysis paralysis and get moving. But PbtA-type games are a whole different subject, I just thought I'd mention this aside.)
As the 'anti sandbox' would be a jerk DM where the DM ran the PCs. "okay, your characters walk forward and fall into the trap...ahahaha...fooled you!" type of DM.
Do not make it black and white. There are shades of grey between.
E.g. the DM has written a loose plot arc. It has an inciting incident, a big event that will happen in the middle, and a climactic conclusion at the end. How the players get to each part (well, perhaps not the inciting incident), and more importantly what they
do in each part, isn't controlled. There could be a lot of things that happen along the way. None of this involves "controlling" the PCs in the ridiculously over-the-top way you describe, but it does involve (more or less) saying, "Hey guys, I have this cool story, are you okay with playing through that?"
Similarly, any time any DM runs a pre-written adventure, that is necessarily not a sandbox. But I know for a fact you know that people play such modules/adventures/APs/etc.
And the DM can leave everything vague....but after a bit of time things will be set, and then it is all just a linear game right?
Nope. It's not a matter of leaving things vague. That's just, as you say, a linear game that isn't pre-written, though admittedly such a game is more responsive to the players. In a sandbox, there isn't anything to
keep vague in the first place. There is just a world with stuff in it and events happening in/to it, and PCs who may or may not get involved. Such a game requires motivated players who won't wait for "the adventure" to come to them. (Quotes because there is no
single adventure!) The players need to actively set goals for themselves both individually and as a group, because a sandbox DM isn't going to
push them through anything. Such a game will bog down and become dull and boring if the players are not active participants asking questions, coming up with ideas, and pushing the situation forward.
Thank you for a list I can understand.
I am glad it was helpful.
Well, I'm at a far extreme myself.
And....look, I can watch 10-20 games played every weekend. Anything I have every typed has been from one of those games: so they do happen. Plus I have seen tons of game played both in real life and online. A lot of things do see do be common....
And yet you keep being told that this is
really, really weird. That people find your descriptions incredibly unusual and even blatantly insulting to playstyles you don't personally practice. In the face of such a response, I recommend reflection. Is your personal experience truly representative? Or have you been witness to unusual DMs, or an unusual local gaming culture? The latter seems rather more plausible considering how
wildly divergent your ideas are from what everyone else in this forum has experienced.