Also, I've been thinking about this.
See, the thing about ASOIAF (the book series) is that it works precisely because it isn't lord of the rings. It turns a whole load of genre conventions on its head. That's why people got into it, I think, because it felt more real and authentically human than the standard "good versus evil and good always wins" style of heroic fantasy.
So if we take this comparison to its logical conclusion, then a sci-fi version of game of thrones would be something which took the conventions of sci-fi as a genre and turned it on its head somehow, which I think is harder because sci-fi has always done dramatic realism. In fact, the way to subvert sci-fi is often to make it more mythological or fantasy-esque, like Star Wars, or to incorporate anti-rational or non-humanist elements, like Childhood's End (although I don't think it's a coincidence that SyFy tried to adapt Childhood's End a few years back).
Weirdly, I think if sci-fi had a game of thrones, it would be something like Interstellar (or rather, the first half of Interstellar)..
Interstellar, despite in my opinion not being a very good movie, is interesting because it strips space travel of a lot of the romance and mythology which science fiction as a genre has injected it with. It presents space travel as it might plasuably be, terrifying, alienating and dehumanizing, something which rather than demonstrating humanity's mastery of the universe actually just reduces them to insignificance against the vastness of the cosmos and the power of the forces of space and time. Travelling space becomes something which warps and distorts human life rather than leaving it intact, something which forces us to think on a cosmic scale and thus reduces both our livespans and the value of our lives down to tiny blinks of the cosmic eye. It can also pose moral challenges, as exhibited by Matt Damon's character on the ice planet, who is both wonderfully despicable and also abjectly pitiable in the face of the nihilistic hopelessness of his position. This is far, far closer to believability I think than the traditional view of all-powerful humans mastering the universe with superscience. Of course, the movie then dulls its own harshness by copping out and suggesting that twoo wub conquers all, but that harsh, bleak message which comes before is about the closest I can see to science fiction giving us the kind of genre subverting kick in the balls which ASOIAF and, to a lesser extent, the Game of Thrones TV series does.
