The adjective is nonsense in this context. Their thesis is that the Neanderthals were outcompeted due to human trade, period. Nothing suggests that the trade was "free" in any sense meaningful to contemporary analogues. If their journal article actually frames it as "free trade" the same way as does this article, then they are subordinating their scholarship to their ideology.
It's unclear, however, why the human ability to organize trading networks would drive the Neanderthals to extinction in any event. Obviously some additional factors must've been involved since otherwise they could just carry on as they had despite their benighted, tradeless subsistence..
"Obviously some additional factors must've been involved"
It was all downhill when they failed to invest in Ipods?
If the Neanderthals traded at all, it was likely "free" trade in the sense that the means of exchange was the barter system, and presumably both parties acted in their own interest.