I personally think the Iliad, Gilgamesh, etc, belong on a "root texts of fantasy" list, not as actual fantasy (genre) books.
One thing that is often missed is that many/most/all stories had fantastical elements until the rise of science and secularism around the late Middle Ages. It was the default genre, so to speak.
If we consider the Gothic romance of around the turn of the 18th-19th century to be a separate genre, among fantasy historians, George MacDonald is often considered the first modern fantasist, with his books Phantastes (1858), The Princess and the Goblin (1872) and Lilith (1895), while William Morris' Wood Beyond the World (1894) is thought to be the first book set in an entirely imaginary world. Around the turn of the century and early 20th century, you had lost civilization fantasists like H Rider Haggard, Edgar Rice Burroughs, and Rudyard Kipling, and a bit later, Abraham Merritt. Alongside those were horror fantasists like Arthur Machen, William Hope Hodgson, Algernon Blackwood, and eventually HP Lovecraft, and then a third sub-genre of children's fantasy with Lewis Carroll, JM Barrie, and L Frank Baum.
However, perhaps the seminal fantasist of the early 20th century was Lord Dunsany, who influenced just about everyone who came after him, including Tolkien and Le Guin. The fact that he, alone, is not on that list utterly invalidates as worthy of serious consideration.
Other important pre-Tolkien fantasists include pulp writers RE Howard, Clark Ashton Smith, and Fritz Leiber (whose long career bookends Tolkien), as well James Branch Cabell, ER Eddison, Hope Mirrlees, and David Lindsay.
Anyhow, almost none of these authors are mentioned on that list, even though they were instrumental in establishing the nature and expanse of the genre.