Celebrim
Legend
Mechanics provide for a sense of fairness, for lack of a better term. They take the decision out of the GM's hands to some degree or another.
This is the same thing as control, at least as a possibility. Whether they have narrator power is a separate issue, and whether they have or want the decision-making capability to exercise the potential control the mechanics give them is also a separate issue. As for that matter what areas the game system gives them control in - 4e for example does give players a large amount of control in combat.
As it relates to the subject of the thread, removing mechanics and relying on GM fiat for things that are supposed to be "the focus" makes sense assuming everyone trusts the GM in that regard. I think that's why it makes sense for Brennan but not necessarily as a general thing, at least from my perspective.
I don't watch Brennan (though my daughter is a big fan of his games) so I can't comment on his DMing style, but I have watched Mercer at work and Matt's style is essentially the same as mine (or what mine would be if all my players were professional thespians). He lets conversations and social interactions play out to create story and fictional positioning, and then usually gives a late social check to determine what the outcome of that play is based on his understanding of the fictional positioning and whether anything is at stake. Brennan could do something very similar, and it wouldn't detract from his point.
And again, for my purpose the issue is that the best way to generate concrete fictional positioning and realized dialogue and narration and to give the players the most chance to participate is essentially just improvisational theater. That's the least abstract game you can play. This is a very different situation than needing to play out a combat between a 40 foot long dragon and four heroes with magical ability. There the least abstract version of that I can probably do involves a battlemap and some sort of combat rules - hopefully rules that provide for tactics and motion and concrete choices by the players.
One thing I disagree with regarding the maker of the video commenting on Brennan's comment is that I don't think 1e AD&D combat was nearly as abstract in practice as he thinks it is, as the 3e D&D rules are just a cleaned-up version of 1e AD&D and if anything were often more abstract especially when it came to things like weapon differentiation.