The claims in the first link, at least, should set off your BS detector. The colors they claim the group could trivially identify are very near identical in terms of 3d distance. By contrast, the colors they claim they could not determine the difference between are extremely far in 3d distance. It's objectively illogical. A quick search turns up that the claims are indeed false, and were fabricated by the BBC for a documentary. Here's [1] an email chain involving various researchers that worked on these experiments. The conclusion is that:
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"The experiment shown in the documentary was a dramatization; the genuine color experiments done with the Himba, some years before, used a different sort of stimuli and a different experimental method; the stimuli shown in the documentary were modeled on those used by Paul Kay and others in experiments on other groups; but in all of the relevant experiments, the dependent measure was reaction time (in finding a matching color or an oddball color), not success or failure.
The BBC's presentation of the mocked-up experiment — purporting to show that the Himba are completely unable to distinguish blue and green shades that seem quite different to us, but can easily distinguish shades of green that seem identical to us — was apparently a journalistic fabrication, created by the documentary's editors after the fact, and was never asserted by the researchers themselves, much less demonstrated experimentally."
I did not do a full literature study of the claims of the article, as that was meant as an illustration of the point, and it was the first relevant link that popped up.
Whatever the alleged fabrications of the BBC might have been or not been for the Himba experiments, similar observations have been made for other groups as well, from Amazonian tribes, to population groups in Papua New Guinea, to Aborigines in Australia. And the MIT research link is discussing a very similar result.
That languages influence how you perceive and see the world has been well studied and is well documented.
I do not think the actual experiments demonstrate this. The experiment the BBC demoed probably would, but it was fabricated. The actual experiments just demonstrate a pretty obvious aspect of learning. If you tell somebody who doesn't play chess all the names of the pieces, and ask him to tell you which is the rook, he's going to be slower and less accurate at it than somebody who plays chess. But there's not some huge epiphany like you can show him a collection of 5 bishops, 1 rook, and him be unable to tell which is different. It's no different with colors, or any new term.
I have personal experience with this, learning Russian. They don't have just blue, but rather a term for dark blue and one for light blue. It's hardly some eye opening thing - it's basically sky blue vs ocean blue. It's obvious and easy, but obviously I will always be slower than a native on a quiz of which is which for reasons that have nothing to do with the colors. Vice versa, compare our speeds in English with 'sky blue' vs 'ocean blue' and I'd be back to winning.
A common trend in the social sciences is creating experiments that aren't designed to challenge one's hypothesis, but confirm it. The publication bias against negative results is probably necessary, but also turning a lot of soft science into a facade.
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"The experiment shown in the documentary was a dramatization; the genuine color experiments done with the Himba, some years before, used a different sort of stimuli and a different experimental method; the stimuli shown in the documentary were modeled on those used by Paul Kay and others in experiments on other groups; but in all of the relevant experiments, the dependent measure was reaction time (in finding a matching color or an oddball color), not success or failure.
The BBC's presentation of the mocked-up experiment — purporting to show that the Himba are completely unable to distinguish blue and green shades that seem quite different to us, but can easily distinguish shades of green that seem identical to us — was apparently a journalistic fabrication, created by the documentary's editors after the fact, and was never asserted by the researchers themselves, much less demonstrated experimentally."
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[1] - https://languagelog.ldc.upenn.edu/nll/?p=18237