To be fair, I believe the published A Game of Thrones was merely that part of the originally conceived A Game of Thrones** that the publishers and GRRM agreed would make a good first novel of the series. As I understand it, he had already completed much of what we now know as A Clash of Kings by that point (and, possibly, some of A Storm of Swords). Which means that he didn't write either ACoK or ASOS in only two years each, as suggested by that timeline.
** - Which would have stretched to the end of what we now know as ASoS.
** - Which would have stretched to the end of what we now know as ASoS.