Sorry, typically assumed by whom?
Alfar are elves (bearing in mind somewhat more nebulous definitions in play) and Dvergr are dwarves. John Lindow is cited in the wiki article as being one among some scholars speculating that dokkalfar may be dwarves by another name, but the baseline linguistic record and standard translations are elves = alfar, dwarves = dvergr. So Gary's was sticking to the mainstream interpretation there.
I think there is more to it than you're suggesting.
I first became aware of this whole thing, specifically Tolkien reimagining Norse elves as the tall & fair concept that was simply not the same as that of most of the public, was when I first read
The Hobbit in the early 1990s as my school library had the annotated version by
Douglas A. Anderson which went into exacting detail about the mythological sources of Tolkien's creation.
Outside of Tolkien, a dwarf, elf, or a gnome were much less distinct entities as we now see them, but all were sort of a faerie type being. For example, in the novella you mentioned,
The Roaring Trumpet, Alfhelm is mentioned but a single time:
“Child of Earth, you weary me.” He stared straight into Shea’s eyes, and once more there was that sensation of an icicle piercing his brain. But Heimdall’s voice was smooth. “From which of the nine worlds do you come, strangest of strangers, with garments like to none I have seen?”
Shea thought. The question was a little like, “Have you quit beating your wife?” He asked cautiously: “Which nine worlds?”
Heimdall laughed lightly. “Ho—I thought I was to be the questioner here. But there is the abode of the gods that is Asgard, and that is one world; and the homes of the giants, that are Jötunheim, Muspellheim, Niflheim, and Hell, or five worlds in all. There is Alfheim where live the dwarfs; (emphasis mine) and Svartalfheim and Vanaheim which we do not know well, though it is said the Vanes shall stand with us at the Time. Lastly there is Midgard, which is overrun with such worms as you.”
Shea yawned. The mead and warmth were beginning to pull up on him. “To tell the truth, I don’t come from any of them, but from outside your system of worlds entirely.”
One of these "dwarfs"
(sic) is encountered in the story, briefly, and is remarked upon by the narrator as looking like Santa Claus.
I suppose that the primary thing is that whether they were called elves or dwarves isn't particularly relevent if you're using a modern Tolkienesq definition of the terms when that was not the case. Basically, even in cases where "elf" was used, the entity that was described would have appeared much as we would identify as a dwarf or gnome.
I'm currently living abroad in rural Ontario and most of my Tolkien library is 1,000 miles away in Raleigh, NC, so it's a bit hard for me to find a lot of these quotations, but there is significant scholarly discussion regarding Tolkien's use of terms and redefining creatures from Norse myth, which included making part of his Noldorian elves "deep elves" which he had taken from Norse myths and was part of the reason we still see the term "gnome" among others used in
The Silmarillion when referring to the Noldorian "deep elves".