The distinction between parody and allusion is pretty blurred, at least in my mind. But you might be right that it's more of an allusion.
Anyway, I was at work before, so I'll post a little more explanation of why I put this in General.
When I read it today, I didn't know what it was about. He put the CD in the microwave, and I was thinking he actually did that. Then it said "don't worry, it's unharmed", and I was thinking wait, haven't I read this before? It sounded most familiar. But I read on. Then it said that he handed it to the narrator, and it was "cold to hold and ..... heavier than before". That's when it struck me what the actual reference was! And the rest just confirmed what I'd already figured out.
Thus, the majority of the enjoyability in it was, to me, the discovery not only that this was a joke, but that it was almost a direct passage from Lord of the Rings. And the entire reason that I enjoyed it was because I didn't know it was supposed to be funny.
And so, with proper classification, an avenue of enjoyment that LotR fans get is blocked. So I put it here, in the hopes that others could enjoy it the same way as me.