I think Tolkien is still relevant to modern day fantasy, but what Tolkien did is entirely different from what numerous modern writers are doing, particularly those like Martin, Abercrombie, or even Lynch and Stover. Even for more epic, quest-oriented adventure fantasy, there is a greater emphasis on character and a lesser emphasis on history and worldbuilding than what you saw in Tolkien.

Jordan might be the only modern fantasy writer I would say can be properly compared to Tolkien. They're different, but the Wheel of Time is the only modern fantasy series I know that approaches its world and its themes in a similar manner. (I freely admit that there could be better examples I simply haven't read.)

Calling Martin the American Tolkien is strange. I love Martin's books, don't get me wrong, but he's not even trying to be Tolkien. Tolkien wrote event-driven myths dipped in history and nobility. Martin writes character-driven socio-political conflicts dipped in primal magic.

I think that modern authors still know (and mostly appreciate) their Tolkien, but Dark Knight may be correct that they don't directly take their cues from him any longer. The genre has expanded significantly over the past thirty years. But it's also fair to say that the concept of fully realized imaginary worlds, still very much active in modern fantasy, owes its popular genesis to Tolkien, and in that respect fantasy has not entirely escaped his shadow.