I couldn't help but notice that the authors were credited "In random order" and am now wondering a) Why not alphabetical? and b) Did they just shuffle the order once or was it "Random until we found an order that happened to match some other criteria we had in mind"
It’s not possible with PDF/A, which prohibits both JavaScript and PostScript in PDF. (These are the only ways I can think of obtaining a random number in PDF.)
PDF lets you run JavaScript (if the PDF viewer doesn’t block it), including on opening a document. Math.random() is available in that environment. JavaScript in PDF allows you to switch the visibility of layers on and off, or to fill the values of text fields. PDF forms sometimes use this to generate likely-unique IDs. Alternatively, PDFs can have embedded PostScript to render contents. PostScript has a random-number function rand built-in. (PostScript support is deprecated in PDF 2.0.)
This is obviously an absurd overextrapolation, and it's unlikely that a significant number of people would actually change their name to exploit it, but the principle is accurate: If alphabetical is used consistently then someone with the last name Zelenskyy will consistently end up last in every list of coauthors, while Adams will consistently come near the top. Even if people intuitively understand that alphabetical ordering is used because all coauthors are equal, the citations will still be for Adams et al., and it's not hard to see how that would give an unfair non-merit-based leg up to Adams over Zelenskyy.
If applied consistently, random order would be a fairly sound way to ensure that over a whole career no one gets too large a leg up from their surname alone.
This is obviously an absurd overextrapolation, and it's unlikely that a significant number of people would actually change their name to exploit it, but the principle is accurate: