How to quote in the title of a thesis in APA style?
I'm not sure that you would need to provide a full citation for a quote that's used that way. 

It's not uncommon to use a small quote at the beginning of an article to provide some "flavor text," as in the picture below. In cases like this, some attribution is given, but the quote source isn't included in the APA Reference list. 



I would think that if you provided the full Game of Thrones passage as a "flavor text" quote at the very beginning of the article (including an informal attribution), that would be enough to get the job done. It's not too different from articles that use a quote from an interview in a title and then to provide the full context of that quote later in the article (e.g., http://dx.doi.org/10.1080/09518398.2010.495091).