(1) The Dunn et al article in Nature is not about language evolution (in the Darwinian sense); it is about language history.
(2) Universal grammar (UG) is a complex set of rules, discovered by Chomsky and his co-workers. UG turns out to be universal (i.e., all known language are governed by its rules) and its rules turn out to be unlearnable on the basis of what the child says and hears, so they must be inborn in the human brain and genome.
(3) Although UG itself is universal, it has some free parameters that are set by learning. Word-order (subject-object vs. object-subject) is one of those learned parameters. The parameter-settings themselves differ for different language families, and are hence, of course, not universal, but cultural.
(4) Hence the Dunn et al results on the history of word-order are not, as claimed, refutations of UG.