Hi!
I'm not sure I agree with your description of Apocalypse World, Poison'd and In a Wicked Age as "Improv" games. They're not any more "Improv" than, for example, D&D3E.
All three games require you to actively pursue the interests of your character. That differentiates them from say, Fiasco, where you're sometimes going to be working against your character's best interests.
In a Wicked Age's tension mostly comes from conflicts between players' characters, and Poison'd is the same to some extent, while in Apocalypse World that's not always the case (although it can be). All three games aren't like, say, Dogs in the Vineyard, which (at least initially) has the players' characters on a fairly unified team, and works fine even if they never come into conflict.
All of these games have explicit mechanistic resolution, i.e. conflicts are resolved by an explict process that references "real life" things like dice or character sheets. That makes them different from some "freeform" games (whatever that means), like Fiasco again, or Archipelago.
None of these games are explicitly competitive, like The Shab-al-Hiri Roach.
In a Wicked Age requires the non-GM players to use more Author and Director stance, from what I understand, than Poison'd or Apocalypse World. In other words, you're more often called upon to make decisions and invent stuff about things other than your own character.
Is this helping?
Definitely helping, "Play your character" is to me a relevant strand of design philosophy.
Now that you mention it, I'm actually not too sure about IAWA and Poison'd, the latter I've never played, but I'd label Apocalypse World and Dogs in the Vineyard as improv games.
The reason is that the principle of accepting and "Yes, and..." is very prominent in their design. This is very prominent in the miss/7-9/10+ move structure (MC makes a move/Yes, but.../Yes, and...) which also counters blocking ("No")
There is a strong emphasis on the MC not to cheat the players but rather accept and build on what they do. Also, when the MC asks questions like crazy, that's an offer that calls for the player to say "Yes, and..." and then answer the question.
The principle of spontanity is formulated in how the MC should never have plan in mind, but rather do what honesty demands, and make apocalypse world seem real, while the players are encouraged to act on their impulses.
The tools might look different, but when entering a game of apocalypse world, one takes on much the same attitude as entering a scene of improv theatre. I think these principles are discernable in Dogs in the Vineyard as well, but on more of a prototype stage. The game follows a sort of here-and-now Input-Impulse-Input sequence of reactions. In my best games, the players just go with what feels right in that particular moment, given the narrative and their options.
He does this, (input from GM) what do you do now? (spontaneous impulse) -> new imput, et cetera.
You get fallout, (input from rules) what do you pick now? (spontaneous impulse)