After watching the newest episode I think I realize what Persona 4 The Animation is; it's an "Abridged" series done right.
Think about it; it's a fast summation of the plot events which points out the more comedic/awkward things within the game itself (the swim trunks, the "humor" dialog options the MC can take while controlled by the player, ect.) while also making it's own in-jokes (Aiya "anywhere" delivery; I get the feeling this isn't the last we've seen of a joke done with the new delivery girl NPC).
Unlike a normal Abridged series though it doesn't feel the need to make a joke out of everything. Which is why I say it's "done right".