I think EGG has stated (in one of the Q&A threads?) that the inclusion of the Tolkien races was merely a marketing ploy. I don't think that's completely untrue, but I don't think it really gives Tolkien's influence proper credit, either.
In "Influence of J.R.R. Tolkien On the D&D and AD&D Games" in Dragon 95 Gary tried really hard to discount Tolkien's influence on the game, to the point of suggesting that European folklore and mythology were equally, if not more, important influences on the demihuman races. Frankly, and with due respect to Gary, I thought his argument was patently ridiculous.
I don't think if you're reading the Elder Eddas or whatever you are going to independently develop dwarves and elves that look so much like Tolkien's. And you sure as heck aren't going to independently invent hobbits, no matter how much folklore you read.
I have no doubt that EGG is not a fan of LotR, and I completely agree that weird fiction from the pulp magazines was much more important to his personal conception of the fantasy genre. And certainly other fantasy sources were also vitally important to making D&D "D&D." But Gary's personal tastes weren't the only input into the game. I don't think Arenson had such antipathy to LotR, and clearly Gary's players were tremendous fans of Tolkien (I believe Rob Kuntz is an avowed fanatic). Maybe it was their influence alone that brought the Tolkien races (and many other influences) into the game.
In any case, Tolkien was and continues to be tremendously important to D&D. I strongly suspect that if the Tolkien races weren't included in D&D at the beginning, the game never would have taken off. As it was, D&D had the good fortune to be born at a time when Tolkien style fantasy was really starting to bubble up all over popular culture -- and D&D was in the exact right place at the right time to really catch on.