Yeah, there is a term. Playing the world. Or, play the world, not the rules.
See how easy that is? I know, WOW! Look, an actual descriptive term that encapsulates how people want to play. And doesn't use infantilizing and negative language.
I mean ... do you wonder why a certain group of people use this term, and is so invested in defending it? If you want to have a conversation with people that are playing different games, maybe start by not using that term to describe their games.
Jus' sayin'.
The problem is how does Play the World differentiate it from any other game?
Just take those 3 words...nothing more. How does it distinguish play from play?
What am I doing in Blades? I'm playing the world.
What am I doing in Torchbearer? I'm playing the world.
What am I doing in Dogs in the Vineyard? I'm playing the world.
What am I doing in Dread? I'm playing the world.
What am I doing when I write up a one-off dungeon for D&D and the players are in token/pawn stance? I'm playing the world.
That phrase just obliterates any characteristics of paradigmatic play that could distinguish it from nearly any other game.
EDIT -
@Bedrockgames , I don't disagree. I mean like I said above, call whatever game whatever...just make sure it (a) represents what is going on under the hood (process and play) and (b) sufficiently distinguishes it from other games that it is clearly different than.
Again, like Spinning Plates with Blades. That absolutely can have a big time negative connotation but it fits (a) and (b). Relentless Grind or Embrace the Suck for Torchbearer also has negative connotations but fits (a) and (b) nicely. I mean...I would say for 4e you could cheekily call it "Skip the Gate Guards"...but that would be way too inside joke for people so something like "Cut to the Action" would be better.
Personally...I don't feel like Mother May I is the best for what we're describing...its not bad in terms of "under the hood", but its not the best. I feel like Play the GM is a better pithy descriptor (though they're both doing different things...the first is talking about authority distribution and the second is talking about the deep responsibility of the GM to conceive and run complex models and resolve player input).