I don't think that including scenes that involve property and trade should be read as somehow advancing an anarcho-capitalist agenda, as opposed to an anarcho-communist one, as though an anarcho-communist author would not include those things in a book he writes. To say that Tolkien advances anarchism in LOTR (to the degree that he does at all, which I agree he does to an extent) isn't to say that everything he portrays throughout the whole story is one enormous picture of the kind of society he thinks is ideal, it's to say that some of the ethical messages that he embeds in the book are messages that especially comport with anarchy. I also am skeptical that anarcho-communists believe that nobody should live in homes, grow things on land, or engage in any trade with one another.
But at any rate, given the time that Tolkien wrote LOTR, I don't think that there was the same taxonomy of the same different kinds of anarchists as there is now, so it might be anachronistic to say he's either one or the other. We do know that when he wrote that he leaned toward anarchy in 1943 he didn't mean that term with any sense that could have been influenced by Murray Rothbard.