I'm going to reserve judgment on the findings themselves until I read the paper (although, having a background in historical linguistics, I've learned to be very skeptical of any claim that posits historical superfamilies.)

However, I will complain about the pop-science intro, because the thought that a hunter-gatherer has some chance of understanding a sentence like the one given is laughably preposterous. An Old English speaker would only barely understand it (just as we would only barely understand gief þæm menn ealdan þisne fýr[1]), to say nothing of the many thousands of years of change between us and the hunter-gatherers spoken of. There is a vast difference between 'two words have a statistically provable correspondence' and 'two words are understood as the same word.'

[1]: My old English is pretty weak, so I take full responsibility for grammatical errors.

Edit: accidentally used 'th' instead of 'þ' in the Old English.