I don't see how it can be a future Earth if there are Dragons and Magic because... well I haven't seen them! It could be an Earth-like Colony where Dragons exist but that still doesn't explain Magic and Walking Dead.
You will need to define what you mean exactly by "post-apocalyptic." The history of Westeros is obviously incredibly long with the Wall founded 8,000 years ago, the wars between Valyria and Ghis 6,000 years ago. It could be a Fantasy world that was more industrial in the distant past but was thrown back into dark ages by some apocalypse. Is that what you meant?
However, there is other evidence from the length of the Winter. Nine-year-long Summers followed by equally long Winters mean that the axial tilt of the planet is very unlike our Earth. There could be an astronomical reason for that, it could even be the result of some catastrophic event on the planet in the past, but apparently George R R Martin has already explained that it is simply due to Magic. For me, that is proof that it is all just Fantasy and it is pointless speculating that it is anything more than that. I'm sure that won't stop someone from developing a detailed scientific explanation for the unpredictable seasons involving binary stars.