The authors in their paper propose a different approach to citing articles, which is to cite the article name instead of the author. This criticism, while humorous, is off-base from what's actually being proposed.

This is not an example that the authors gave, but you might write something like "On the Origin of Species (1859)" instead.

This joke also misses the point in that a follow-up anonymous article would not, to match the author's intent, reference the authorship of previous work. The whole point is for each article to stand on its own, so referencing yourself pseudonymously as the author of a previous article does not achieve the goal.

I don't want to be "that guy" who takes the humor too seriously, but I worry from the comments so far that people will conflate the humor and the actual proposal. The overall aim and proposal of the article is to find a way for papers to be judged individually on their own merits, rather than on the merits of their author, the author's institution, the author's nationality, or the paper it was published in. This is a worthwhile goal even if we cannot see a serious means by which to achieve it.

To be fair to the jokes, while reading the article I was unsure if it was satire. I'm still not completely sure. I believe the authors are sincere in their belief in anonymity as promoting merit, but I remain unsure whether they think their proposal is realistic, and whether or not they are making some kind of meta-point about the state of scientific review by observing how far away the current review process is from one that would be (as best as we can make it) unbiased. That is to say, upon reading the paper, the idea of implementing their anonymity proposal seems ridiculous - and this realization may be partly the point of the paper, to get the reader to realize how many different points in the editorial process depend on the author's identity rather than the material's merit. It does not strike me as satire, because the work takes itself seriously, but it may seem like satire because of how large the gap is from where we are to a meritorious review system.

"Ha! It would be ridiculous for work to be reviewed, published, and promoted purely on its own merit, rather than based on the legacy of the author."

On the other hand, it's hard to say how well a fully anonymous system would work. Human biases often serve a useful cognitive function in allowing some filtering operation to be performed more efficiently, albeit with less accuracy. A random lunatic who claims to have invented a perpetual motion machine is likely to be wrong. It's possible that devoting equal review time to all claims and all papers would lower the sum value of scientific output. If the volume of scientific material is too great to comprehensively review, from any given observer's standpoint, then a system that relies on identity as a heuristic and is slightly less meritorious may be strictly better than an anonymous system that is slightly more meritorious, for example. Society might have a different goal for the output of the scientific process, which is to maximize the discovery/promotion/publication of useful scientific output - and that is a different goal than judging individual work fairly.