The article doesn't say what the headline says. At all. Never in the article does it say that "our capacity for language emerged 135,000 years ago".
What the article says is that they have genomically traced our species back to around 135,000 years ago to the point where we started splitting off in different groups, and as we all have the capacity for language we must have had it at the point of split as well (before that all could be said to be in the same local group. Possible, what with those population bottlenecks and everything).<p>There's nothing in there saying there wasn't language before, nor why it shouldn't have been present much earlier. Early enough that e.g. Neanderthals could equally well be covered.