"but that they are not encoding any meaningful information that a human being produced"
I was sort of with you up to that point; I don't agree, but I was with you. However, now I would say you need to read the article more carefully, as the entire point is that they do indeed encode something human-produced and usable. If you use Unix, you've almost certainly got the decoder for that number sitting right on your disk right now, it doesn't get much more concrete than that. Without that, you're missing the whole point. They aren't randomly generated at all.
Guess I might as well spell out the other objection I have, which is that you're subtly begging the question. You prove that the idea of owning a number is silly because the idea of owning a number is silly in your last sentence of your first paragraph. Let me give you a much better argument: flip your argument on its head, and say that of course it's perfectly sensible to own numbers.
All but the smallest works translate in any reasonable encoding scheme into enormous numbers, numbers that would simply never be chosen randomly. There 0 chance that sitting here and stringing together "random numbers" will ever produce anything like a movie or picture or even coherent sentence, that doesn't already exist in the encoding scheme. (Not literally 0, depending on the circumstances, but close enough.) Therefore, the actual problem is that it does indeed make sense to own numbers; in an infinite space when we are all choosing umpteen millions or billions or trillions or well beyond that of digits, one can very plausibly stake an ownership claim on the grounds that it is clear that if somebody else ends up with the exact same number, they got it from you.
Therefore, since it is sensible to own numbers, the objection that it is not collapses and then the rest of the argument against ownership does too.
As I said, I don't actually agree with that line of thought. There are a lot of intricacies in the issues of encoding, and some other objections I'm leaving out, but it's still a stronger line of argument. My feeling are more related to the classic bit color essay: http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php If that doesn't seem related, think more; it is, it very much is.