The claim is dubious.
The similarities between the two creatures are weak, and Gygax (who created the intellect devourer) was unlikely to have been a fan of LeGuin or to have drawn inspiration from her work. It is possible that Mr. Rooney is a LeGuin fan who plays D&D, theorized about a connection between the two creatures, and then presented his theory as fact. This is not an uncommon practice on internet fan sites.
Note: LeGuin's monster was actually called a shadow. "Gebbeth" was the word used to describe those forms it used to deceive people; the word was likened to the word "puppet." I'll use "gebbeth" for the creature in this answer for simplicity.
The similarities in the two creatures' nature could be incidental and the differences are significant.
The intellect devourer is a corporeal, biological entity that controls people via its psionic abilities in order to feed. It has claws, but prefers its psionic attack. The intellect devourer is not, by its nature, something that must be summoned into existence and there is nothing to suggest that it hunts a single victim across hundreds of miles to the exclusion of other prey.
The gebbeth is a supernatural being that must be summoned into existence (summoned by accident in the case of Ged, A Wizard of Earthsea's protagonist) and which has the single purpose of hunting down and possessing a specific person. It doggedly hunts Ged with a mobility the intellect devourer doesn't have (at multiple points it chases Ged across large bodies of water). On no occasion does the gebbeth use anything like a psychic blast, preferring the use of its talons in combat. Its' description is suggestive of some kind of undead—possibly incorporeal, or semi-incorporeal.
'The body of a gebbeth has been drained of true substance and is something like a shell or a vapour in the form of a man, an unreal flesh clothing the shadow which is real.'
The intellect devourer can be killed with weapons or spells like most monsters. By contrast, the gebbeth could not be killed. Only by giving the gebbeth his own name and merging with it does Ged end its pursuit.
Both beings seek to take over and control someone, but that's one similarity among many significant differences. In addition, literature and folklore (and Hollywood, an often forgotten source of inspiration for D&D) have other examples of creatures taking control of someone that could have inspired the intellect devourer as easily as the gebbeth.
The gebbeth's appearance is unlike like that of the intellect devourer.
Mr. Rooney's post is somewhat inaccurate in its characterization of the history of the intellect devourer's appearance. Eldritch Wizardry does not have a drawing of the creature, which means Trampier's Monster Manual depiction is probably the first published drawing of the monster; however, Mr. Rooney's assertion that "only the legs are described" in Eldritch Wizardry is wrong. The body is described in more detail than the legs.
The appearance of an intellect devourer is frightening in itself, for they have no apparent head, being merely a ball-like body of sooty black poised upon four legs.
So the intellect devourer was originally corporeal, headless, and quadrupedal. Its later appearance created by Trampier did change, but not drastically so, with a sooty black ball becoming a brain. The creature does not change its appearance in the course of taking over a victim.
By contrast, LeGuin's gebbeth, began as a child-sized, nondescript "clot" and slowly morphed until it wound up looking like Ged, its victim. The "clot," which had talons (how many is never specified) with which it attacked Ged, could conceivably be imagined as similar to Eldritch Wizardry's intellect devourer, but it could also be imagined as quite different. LeGuin's description is rather vague. Mr. Rooney's claim that LeGuin envisioned the gebbeth as a tardigrade is supported by illustrator Charles Vess, who worked with her. Whether a tardigrade looks like an intellect devourer is a subjective question, but I don't think it does--Mr. Rooney says it doesn't have a head, but it looks to me like it does. In any event, that's irrelevant since the sparse description in the book does not really specify any specific features of the animal LeGuin was thinking of. Of course the gebbeth's later appearance is nothing like the intellect devourer or the tardigrade.
Gygax isn't talking, but he never mentioned LeGuin when he was.
I could not locate any quotations from Gary Gygax speaking about influences that led to the intellect devourer or referring to LeGuin in any capacity; nor can I find similar quotes from anyone who knew or worked with him. Appendix N of the AD&D Dungeon Master's Guide gives us a list of 29 authors who Gygax said were "of particular inspiration" to him. LeGuin is not on it. Frankly, Gygax's oft-stated preference for swashbuckling, high adventure fantasy in the vein of Robert E. Howard suggests he wouldn't have liked the more philosophical and action-light fantasy of LeGuin. I'm not the only one who holds this opinion--Gygax's preference for styles of fantasy very different from LeGuin's has been the subject of some interesting articles--this one and this one are of particular interest since they discuss why Gygax would have been unlikely to find inspiration in LeGuin. Gygax himself typically cited pulp fantasy authors as his primary influences, as in this interview when asked about his influences:
Mainly Robert E. Howard, L. Sprague DeCamp, and Fritz Lieber. The magic system is based on Vance's work.
Tolkien--one author in Appendix N who is decidedly not a pulp fantasy writer--was not an author Gygax enjoyed. From the same interview, when asked about Tolkien:
I'm not a big Tolkien fan, though. I did love the movies, but I yawned through the books. I found them very droll and very dull.
Obviously Gygax lifted things straight from Tolkien (so obviously and extensively that he could not exclude Tolkien from Appendix N), so why could he not also borrow from LeGuin? For one thing, Gygax later claimed he borrowed elements of Tolkien only to attract Tolkien's large numbers of fans to the game. From Grognardia:
At the time, The Lord of the Rings was a huge hit in fantasy fandom. Gygax later claimed, and I believe his claim, that the game wasn't much influenced by Tolkien and the references were (mostly) an attempt to connect the game to the then-faddish interest in the Professor's works.
Further, Gygax's lifting from Tolkien was blatant: balrogs, ents, hobbits (later changed to balors, treants, and halflings after the Tolkien estate sued). Elves, dwarves, orcs, worgs, and rangers also were thinly veiled or not veiled at all. So if he wanted to lift the gebbeth--either because he liked it or just to attract LeGuin's nowhere near as numerous fans--why not do so more directly? He copied Tolkien's monsters almost directly from the books. Why change LeGuin's creature so much that it's scarcely recognizable? This of course assumes he even knew about the gebbeth or had read A Wizard of Earthsea and used it as inspiration for D&D, which is uncertain and probably unlikely given his preference for pulp fantasy.
So there is really nothing conclusive, or even very compelling, to suggest LeGuin's gebbeth was the inspiration for anything in D&D. Of course I cannot prove a negative when the creator of the intellect devourer is deceased, but the weak connections between the intellect devourer and the gebbeth and between Gygax and Le Guin permit us to dismiss this claim barring the discovery of some extraordinary piece of evidence to the contrary.