The more I engage with this game, and compare it to other games, the more I appreciate its genius.
The Core Mechanic
The core mechanic should seem familiar to people who have played D&D - it's a little less granular - instead of saying "I shoot him" you say things like "I point my gun at him and make him back down" ("going aggro") - but the idea is the same: you want to try something in the game, you usually have to roll for it. A lot of the modern collaborative-story-heavy rpg's have moved away from this traditional approach, but AW makes it sing. How?
Any move you do, you roll two dice, and add them together, and maybe add some modifiers if your character is good at that thing or whatever. And you try to get a 7+. Still, standard roleplaying, right? Roll dice, add modifiers, try to beat a target number.
Not quite: if you fail a roll in AW (6 or less), something bad happens. Where it just would have been a 'whiff' in D&D, here additional trouble is piled on. And if you ONLY get 7+ - if you don't get 10 or higher - you get a mixed result. Something good, something bad. Or something mediocre.
Bottom line: whenever you roll the dice, something happens. You don't get that feeling of "I might as well have just skipped my turn."
Historical note: this is a bit like Otherkind Dice and Ghost/Echo. There, you rolled multiple d6's, and some would be whether the good result happened or not, and some would be whether a bad result happened or not, so it was very possible to get mixed results. It was still possible to whiff, though - nothing good, nothing bad. AW fixes that and streamlines things.
Game Moderating As Maintaining A Collection of Threats or Dangers
There's a line in the AW book that says it calls for one method of GMing - that the entire game is built upon it. I didn't understand what this really meant until recently, when I was looking at another game: Danger Patrol. (A free game you can play right now, google it.)
A quick naive non-exhaustive taxonomy of roleplaying methods, divided by the kinds of prep you do:
* The sandbox: a map with hidden stuff in it. Could be a dungeon, could be a wilderness, could be whatever. Older D&D modules were like this: a big map. Where do you want to go? What do you want to do?
* The railroad: a series of encounters that the players will meet in order, providing they play nice and don't say anything like, "What? Save the world? I didn't sign up for that." This was how I used to GM, because I wanted to tell a story in a fairly linear order. Modern D&D modules are more like this - because you can only fit a couple encounters in in a session and they take a lot of planning, they may have maps but the maps are linear.
* The relationship map: instead of it being about the terrain, it's about the people and what they want from each other and who the players know. GMing this requires some creativity. "Okay, the players are doing this. How do my characters feel about that? What are my characters going to do now?" To make this work, the characters have to have incompatible wants, so that a story will happen. In a Wicked Age and Smallville are modern examples of games that rock this method.
* Threats or dangers. There's just a list of bad stuff that could happen or is happening. Could be a character wants something from someone and that's going to lead to problems - a bit like a link on the relationship map. Could be a bomb in the building. Could be a stormfront. In Danger Patrol, Ghost/Echo, and Poison'd - these troubles are written down on cards or post-its for all the players to see. When a player tries to fix one of the troubles, and gets a 'Yes, but...' on the dice - the trouble might go away or be mitigated, sure, but another trouble is plopped down, on another card. The whole thing organically grows and shrinks. The players have the freedom to do whatever they want and the game responds appropriately. And with DP, GE, and Poison'd, it would never occur to you to remove the index-card-danger mechanic. It's just part of the game.
With Apocalypse World, however, the dangers and troubles (called "threats" in AW) are (sort of) secret. The moderator keeps track of them on their own sheet of paper and doesn't show the players. So a GM might approach the AW rules and say, "Well, I'm going to skip that part." But that would be like removing the board from a board game.
So that's why the rules say the game calls for one kind of GMing.
And, just as a side note, this method of GMing? One could make a computer game out of it. The creator of the game would need to prepare ahead of time the things that ordinarily are made up in play - which is a lot of prep: most people would only see a fraction of the content unless they played multiple times. But there'd be a lot less prep than, say, trying to make one of those choose-your-own-story books. (And it's much more promising than my experiments in having intelligent agents with wants that are supposed to come into conflict - which is the relationship-map method - that was one I banged my head against for years with almost nothing to show for it.)