A Song of Ice and Fire a made-up world of roughly medieval technology who are fighting a centuries-long war against a non-human evil. It definitely focusses on certain things not in LotR past that, but at its base, its genre hook is clearly one paved by LotR. The slew of "fantasy = made-up medieval civilisation fighting evil" book series all are at least somewhat inspired by LotR. (ASoIaF also has some direct allusions to LotR, just in case you doubt that Martin is paying the books at least a little homage.) Whether or not you like LotR (and there's plenty to dislike) they're certainly pretty much responsible for the epic fantasy genre. It's to the point where Martin would probably have not wanted to set ASoIaF in a world with, say, 19th century technology just because fantasy fans would be less hooked in by it - they expect something a little more like Tolkien.
Harry Potter is not that style of epic fantasy, and it's not what is being talked about when people make comments like that. (And I'm not familiar with the third.)