So here is the issue that the actual article discusses. In generating sentences, you have grammars with rewrite rules like

  PP(Prepositional Phrase) := P(Preposition)NP(Noun Phrase).

In such a rule, the preposition is the head. There is an assertion that languages have the property head-first or complement-first. In this case, the complement-first rule would instead be

  PP := NP(Noun Phrase) P(Preposition)

So in head-first languages, we would see:

  PP := P NP
  The man is PP(in the house)
  VP := V NP
  I VP(ate the bird)

And in complement-first languages, we would see:

  PP := NP P
  The man is PP(the house in)
  VP := NP V
  I VP(the bird ate)

The article states that if head-first and complement-first were robust, universal features of languages, then we would expect the evolutionary model to show that the appearances of word orders demonstrating these features are dependent on each other across language families. However, it does not show this across the language families. It only shows that certain word orders created by head-firstness or complement-firstness are dependent in certain language families.

I hope this was a decent enough explanation and easy for others to follow. I was a Linguistics major, so it can be hard for me to explain it well and in an easy to understand way.

[edited in an attempt at formatting] [edited to provide more examples]