The DM decided what the goals were, what happened on success and failure. They also decided which skills were appropriate. When running a skill challenge the DM was supposed to let the players know the goals and appropriate skills, it was then run similar to a combat with initiative and every PC needing to do something on their turn. Players could use a skill the DM hadn't thought of if they could convince the DM that it could be useful.
In my experience to turned out to be very detrimental to creativity and I stopped using them in my home game. They became very boring and frustrating for people I played with, it had a tendency to kill role playing and alternative approaches to overcoming obstacles. If someone came up with a solution that should have ended the challenge immediately, it still only counted as 1 success. It became "Okay, Bob is good at skill X so he'll use that. Sue is good at Y, Kim what is your PC good at?"
Would you describe D&D combat as the same? People taking turns rolling dice to see what happens, and trying to angle to do what they're good at?
Does that structure that the combat rules provide chafe in the same way as skill challenges did for your group?
The thing is that after a while people would literally groan at the table when someone announced we were starting a skill challenge. So I'm not sure I can disagree more with "procedures make the game inherently better." In my experience they are just as likely to make the game worse.
Please drop the "inherently better" stuff. No one is saying that. Not better or worse, just different.
But... some don't agree that the impact has been a less "complete" game. I don't think anyone objects to discussing it... but this seems more concerned with the fact that some in that discussion come to a different conclusion than others.
So D&D now delivers a wider range of possible adventures, right? A greater number of experiences (adventures) versus a core experience (site-based exploration).
Does that wider range require a greater number of structures to help deliver those experiences?
Has the game delivered that? Are the suggestions in the DMG on how to do these things sufficient?
Does "the GM gets to decide" suitably replace any and all such structures?
If we consider "GM decides" as a structure, then aren't all games that follow that structure similar in the same way as all site-based exploration games are similar? Have we simply replaced one core experience (site-based exploration) with another (GM's-fiction exploration)?
So GM styles is the determiner of difference?
Not solely, no, but I'd say it's a big factor. Take a player from Critical Role and have them jump in on Dimension 20, and they'll hit the ground running. Take them and put them into a B/X game and they'll need some adjustments.
Though I don't know if this is actually GM style... as
@Vaalingrade pointed out, Dimension 20 is more madcap than Critical Role. That's more a tonal difference. And there are differences in genre between the two, as well. Those seem more about style.
What I'm talking about is the actual structure of the game and how it works and how I as a player experience it.