Honestly, I feel like most of the article is throw-away material. They're claiming to have "derived" syntax and grammar from a simple lexicon, which as far as I can tell consists only of referents. In reality, they are just artificially imposing their own ideas of language on top of animal calls. Yes, the calls do convey meaning, but that does not make a language.

It's like gluing a bunch of toothpicks to steel girders, then saying you can build a bridge out of toothpicks.