Originally Posted by VanBuren
Dorne wasn't part of the realm until two centuries after the fact, so it's not being counted as one of the Seven Kingdoms.
Appendix to A Feast for Crows
notes that "Dorne was the last of the Seven Kingdoms to swear fealty to the Iron Throne."
I think the Riverlands must be the non-kingdom. There was a king in the North, a Storm-King, a king of the Reach (which House Tyrell was steward to), a kingdom of Mountain and Vale, the kingdom of the Iron Islands, and--I think anyway--a western kingdom.
Also, I love how in that appendix: