Well... using DTRPG as the pointer.
The Sword, the Crown, and the Unspeakable Power is a PbtA game that is supposed to be inspired by AGOT. I've tried it. I was not impressed by it. I feel like it's pretty stale as far as PbtA goes. It doesn't really PUSH very hard, IMO. There are playbooks, and hints of a setting drama, but it's very generic. There's way more world-building in Legacy: Life Amongst the Ruins, including House politics, and it isn't even made to be an AGOT game.
World-books based on Legacy: Life Amongst the Ruins might be more/better in that regard. These really evoke a House, House politics, and playing as scions of a House in a long-running, generation-spanning game.
Free From the Yoke (based on the historical Rus when they were freed from the Tartar Yoke) and
Legacy: Godsend (where your individuals are avatars of the god, like the Red Woman)... these might be better. "Free from the Yoke" might be best. Just replace the Tartar Yoke with the Targaryens (especially since the game doesn't specify the Tartars, and instead has a generic "Empire" that you can fill with your own ideas), and you have something that could be like the 7 Kingdoms.
In
Age of Anarchy, you're playing nobles in the court of a Lord in Norman England. Support your lord, sabotage rivals, etc.
There's
Houses of the Blooded, of course. That's been around a while. He wrote it as the anti-D&D. Instead of being house-less Murder Hobos, you're playing the leaders of noble Houses. You have peons who do the murdering for you. That's the point.
Oh, and the
DUNE RPG from Modiphius... although the House side of the game is poorly implemented at this point. Nascent. They should flesh it out later, and the potential is there for greatness. It just ain't there yet.