Allegory, Tolkien said, 'resides ... in the purposed domination of the author' (FR xxiv). I don't know why I never saw until the other day that this description so closely matches what he says about the Ring, but lately I've been working on a book about the Ring inter alia. So perhaps that allowed me to see this phrase differently. We need think only of the incantation contained in the Ring verse and inscribed on the Ring itself (FR 1.ii.50); of Elrond's words to Glóin that 'those who made [the Elven rings] did not desire strength or domination' (FR 2.ii.268); or of Galadriel's warning to Frodo that to use the One Ring '[he] would need ... to train [his] will to the domination of the wills of others' (FR 2.vii.366).
I could be mischievous and suggest that the Ring is an allegory of Allegory, but that would be too meta. It would also be wrong. But I guess he wasn't kidding when he said he expressed his dislike for allegory. So were all stories in Mordor allegories?