While I agree with you that ‘plagiarism’ is an inaccurate word, I don’t think it’s an unreasonable one for someone to have pulled instead of ‘infringing’. Depending on the resulting nature of the works, it is absolutely possible that any stories written for this challenge would infringe the original author’s copyright.
The biggest crux would be whether the resulting work is considered derivative or transformative; generally speaking, copyright includes the right to produce and control derivative works, although there are exceptions (and other nuance). I do think it’s likely that the works in question would be considered transformative rather than derivative, which helps - that’s the primary legal protection for fanfiction, for example, and I trust the opinions of the lawyers who founded the AO3 in that regard - but even then, as much as I think it’s the most important argument here, it’s also not always enough to clear a work as non-infringing.
The other side, of course - and maybe this is just because of my long time spent in online fan spaces - is that doing this to someone else’s story without permission, even an apparently abandoned one (and let me tell you, I have seen fics I thought abandoned for over a decade that the original author came back to and finished), is incredibly taboo in most of those fan spaces because, among other reasons, it’s just really fucking rude. That’s a cultural norm, of course, rather than an objective fact, but it’s a huge part of my initial objection to the challenge as it was initially presented, and I can only imagine that there are others around with a similar background to mine who had that same influence.