Today The Nation published an article by Michelle Dean called "Is 'Game of Thrones' Escapist Enough?" Dean looks at Game of Thrones through the lens of our historically demonstrated appetite for escapist entertainment during bad times and, compared to past escapist utopias, finds it wanting.
And if you're looking for Great Depression-style, good-guys-in-white-hats, only happy endings fare, she's absolutely right. But I don't think that sort of escape would have found many takers in today's world anyway. Instead, I think Game of Thrones demonstrates a newer, postmodern sort of escapism that better resonates with people today.
Ned Stark, for example, is one of the characters people are more likely to want to identify with. We get to hope that we would act as honorably as he does, while at the same time we imagine we could have handled the Westerosian politics more skillfully than he did and thus end up keeping our heads. Likewise, Tyrion is a fascinating character because he is deficient in the martial virtues prized by his culture, yet he manages to make his way through the world more successfully than some characters who better embody the ideals of Westerosian manhood. He is a dwarf among (sometimes literally) larger than life men, and yet he succeeds when he "should have" failed.
I think Tyrion, and also Arya (among others), demonstrate the escapist ideals of Game of Thrones: By any rational analysis, these are characters who should have been completely crushed by the events of their world, but instead they're able not only to survive but to take action which significantly changes the world around them. In a time when so many people feel helpless in trying to improve this situation, the power of this fantasy cannot be understated.