I pretty much quit playing the KID as Black, but if memory serves me right, I believe Vigorito, in his 2-book series on the King's Indian from a couple of years ago, mentions that 13...a5 is the main move now against 13.a4, and that 13...Ng6 14.a5 gives Black problems these days. You might want to look into 13...a5 instead of 13...Ng6, which results in the position you are displaying. Looking at Amazon, and viewing pieces of the book I mention, it appears to begin on page 64. Just about every line in the analysis of 13...Ng6 (pages 64, 65, etc) seem to be very strong for White.
Give 13...a5 a serious study.
I don't get it. I play this position all the time and I always lose as Black although Black has a fair bit of play on the Kingside.
Any suggestions?