Fantasy
We've never met anyone who wanted to argue that A Game of Thrones isn't fantasy. It takes place on an imaginary world, it includes dragons and direwolves, and the seasons last for years. So, yeah: fantasy.
There are all sorts of things in this book that aren't exactly fantasy but that are associated with the genre. For instance, a lot of fantasy books have a pseudo-medieval European setting, with knights and castles and no iPads. (This is actually changing recently as new fantasy authors base their worlds on different elements of history, such as Chinese history or Arabic legends. Keep your eye out for these.)
But what makes Martin's books special is that they take all of these typical elements – dragons, pseudo-medieval castles, etc. – and mix them up in a different way. So, typically, we'd get a story where a knight and a wizard ride out of a castle and kill a dragon. (Yeah, we've totally read that book.) But instead, here we get a world where there isn't much (or any magic), and where the biggest danger isn't a dragon but the schemes of other nobles or even a measly infection.
A Game of Thrones is a lot more historical than a lot of fantasy novels; Martin didn't just take the props of a medieval time (oh, let's throw in a sword and a castle). Instead, he really goes into the details of what made that time so terrible (no penicillin, people dying a lot younger, a lot of violence with no real law system to stop it, and again, no iPads). And only once he's created this realistic world, that's when he starts to bring in more magic (dragons!).