I have read the books to much xD
There's only nine recognized Great Houses and who's included is pretty standard.
But the test does not ask for Great Houses (in-world definition), but for major houses. And in this regard, the selection of those nine is fine. However, I don't think selecting Dragonstone as the Targaryen seat is accurate: they had holdings in Valyria for centuries, then ruled Dragonstone for just 125 years, then in King's Landing for three centuries, and then were exiled. King's Landing, therefore, was their seat more recently and for more time than Dragonstone, and it's a better answer (or at the very least, should be accepted as a type-in)
Surprised to see the Frey's weren't on here.
Also, "Gates of the Moon" should be accepted for Arryn, since it's their winter seat.
The fact that Dragonstone was traditionally given to the heir of the crown exemplifies that it was no longer the seat of the king, or his court, or the center of the government. Eventually the Targaryens held other castles too, like Summerhall, but their indisputable seat of the family was King's Landing and the Red Keep.