In fairness, they are using this as an opportunity to wonder why all fantasy and historical movies seem to have British accents. That seems a question worth considering.
But using HBO’s Game of Thrones as a vehicle for raising the question is silly. They had to give the show a British accent — the book has a British accent. For whatever reason, Martin wrote all his Westerosi characters (except perhaps the Dornish) to speak British English rather than Martin’s own American English. If he went to the work to make the book British, how can the adaptation do otherwise?
If they had asked why Martin felt a need to make the characters in his retelling of the War of the Roses speak with modern British accents, that would have been another question worth considering. After all, a modern American accent is no further from a 14th- or 15th-century English accent than a modern British accent is — they’re both equally descendants of medieval English. A modern-American-sounding Robin Hood, for example, is just as authentic as a modern-British-sounding one.
But asking why American TV producers made a British-sounding adaptation of a British-sounding American book just makes them look like they didn’t do any of their homework before going to print.