title_body: Features of unlearnable languages
upvoted_answer: If you search for the researchers mentioned in the article, you can find some of their research papers. In those, they describe their methodology. In one paper that I looked at briefly, for example, they mention that they varied the consistency by making the placement of determiners random. (This is actually also mentioned in the Motherboard article).
  
  Their research seems to be focused on finding out how children can learn languages, and what universal features of languages there are, so they up the difficulty of their experimental mini-languages by using rare elements, such as OSV word order (most (Western) languages use SVO). Discovery that some mini-languages are unlearnable is thus a side-effect of pushing the limits as to what are possible human languages. From a cursory glance at several papers I'd think that you can make a language 'unlearnable' if you add some random variation and choose a lot of rare grammatical features.
  
  PS: in the Motherboard article they actually give a reason why no documentation of Sillyspeak is available: they want to avoid it 'escaping' into the wild, as its purpose is to be a completely unknown language to the subjects of the experiments.