Huh. Just googled that line and yes, the whole thing is a gambit by black, and yes, the whole point is to sit on c5 and work on white's e pawn.
I guess this is an attempt to avoid the Pirc-type positions where you play Re8 and/or Nd7 and then push e5.
I don't play the 4 pawns variations (KID only as white here) but generally speaking, white does not want to liquidate the centre. White wants to suffocate black with space advantage, i.e. playing d5 and not exchanging.
Na6 is a standard move, to commandeer the c5 square.
That knight is also useful to try and discourage white from being too frisky and 0-0-0 and pawnstorm black in the kingside. (other lines of the kid, not in your positions).
In your second diagram I would think black has obtained what he wanted: all his pieces are free. Sure he has not centre, but that's why the KID is a hypermodern opening.
So, I'm flipping through one of my old chess books and I came across some moves that I am having trouble understanding. The author is discussing different options in the King's Indian Defence and throws out the following: "The Four Pawns Attack (4.e4 d6 5.f4) is White's most overtly aggressive system. Black must either choose an early ...c5 or prepare ...e5 with ...Na6."
I'm wondering how ...Na6 prepares ...e5. I'm assuming that he is talking about something like 5...0-0 6.Nf3 Na6 7.Be2 e5. Then if 8.fxe5 dxe5 9.d5, black can follow up with 9...Nc5.
My two questions are these
1. Is this the point?
2. In a line like this, why can't white just respond to 8.fxe5 dxe5 with 9.Nxe5? I ran this through the Shredder opening database and the games where this has been played seem to agree that this is a critical issue. After 9...c5, white can just play 10.Be3 and follow up 10...cxd4 with 11.Bxd4. In this position, I feel like asking "What is that knight doing over there on a6?"