This is a more general question: why would linguistic Olympiads and competitions in general use for their puzzles real, non-obscure languages, which someone among the the contestants may already know?
I know nothing about NACLO in particular, and I will offer some speculation which I still think relevant.
- Oversight: “meh, noone will know Turkish”. Which of course is pretty lazy. And that’s why fieldwork linguists pick their own language of interest, which they can be reasonably sure noone will know. I was never a fieldworker, but when I set assignments, I’d make a point of using Tsakonian. I’ve seen a fair few Australian Aboriginal languages in assignments. I’ve also seen Klingon, although I don’ t think that’s nowadays a more obscure choice than Hungarian.
- On the other hand, if the puzzle or quiz is not just about “work out what this means, and give a one sentence answer” but “give an analysis of this data”, then the choice of language doesn’t matter in most cases. Maybe 0.5% of the people sitting the Olympiad know Turkish or Hungarian. The number of people able to come up with a cogent linguistic analysis under exam conditions will be a smaller proportion: native speakers aren’t linguists out of the box. Admittedly, not massively smaller.
- And if you’re going to write a non-trivial question, making up a toy language is not going to cut it. You’ll want a language whose mechanics have been worked out, so that you can ask intelligent questions around it. But honestly, if you’re picking Hungarian or Turkish over, I dunno, Lakota or Mandinka, I go back to point #1. Pretty lazy.