I mean, I have little doubt that Arneson read Tolkiem, for that matter. The specific way thar "dungeon" gets used I'm the Hobvit happens to be exactly the way it has been genericized by D&D...but that's not what the word has meant in Engliah prior, Tolkien was playing his etymological games and looking for alliteration in a poem. I have zer o doubt that's the source of the term for D&D. There were a bunch of other Old School D&Disms in the Hobbit that I noted on my recent listen, very specific terms, bit that's the one that stuck in my head.Well, on that the use was certainly more diffuse, and Gygax didn't originate the term. The idea for "dungeons" came specifically from Arneson. It was his idea to have the dungeons underneath the castle as a place for the players (using individual characters) to adventure, and then he showed it off to Gygax. Blackmoor, Greyhawk, et al.
And so I find that double unlikely- first, the idea of "dungeons" beneath a castle had widespread usage prior to Tolkien. Second, Gygax didn't "borrow" it from Tolkien. He used it because of Arneson. It would be an example, unless we had more, of people reading Tolkien back into D&D.