1) The writer tries to finesse Geoff Pullum's ongoing lament (see here, here, and here, inter alia) about what he [the Times writer, not Geoff Pullum] calls "the apocryphal story about the Inuit and their 40 words for 'snow'". The point, according to the author, is that regardless of its truth, the story is "a revelation of what we call 'a sense of place'". This sort of thinking strikes SC as weaselly; surely the empirical truth about whether or not different languages are really associated with different mindsets is relevant to the question of whether or not they tell you anything about the thinking of the people who speak them.
2) There is an irritating morality play that the author tries to set up between a group of linguists who allegedly "dismiss salvage efforts...as futile exercises" and linguists who "will tell you that every language has its own unique theology and philosophy buried in its very sinews". Is it really possible that there are no intermediate positions on the merits of preserving small language communities? On the one hand, it's certainly true that constructing your theory of language around just a few languages is going to miss a lot of important facts. Subject-verb-object and subject-object-verb combine to form a large majority of the world's languages' structures, so every time we lose a language of the rarer types, a real opportunity for study is lost. On the other hand, SC has stated before that he "cannot and will not get upset about the idea that other people expect you to be able to share meaning with them in an efficient manner", and that means teaching people who can't communicate with the majority to do so. There is a difference between insisting that people who want to advance economically learn the majority language and pursuing a campaign of actively suppressing minority languages, but the article's author isn't interested in the idea that such positions could be nuanced.
3) According to the article, "[A]mong linguists, the sorrowful story of the 'last speaker' is practically a literary genre". And some of these "last speakers" aren't always really the last, at least in the mind of the author. The article seems to be condemning the man who went by "Red Thunder Cloud" for not really being an Indian; however, if he spoke the language after all of the native speakers died out, and nobody else could do so, then SC can't see what's wrong with identifying him as the last speaker of the language prior to his death. If the author seriously means that only people who are genetically related to the original language group count as "speakers of a language", then it's impossible to distinguish between speech and race. Given that SC has friends of a variety of races whose English is uniformly better than their command of their ancestral languages -- many of which they have only learned in school -- your host thinks that this opinion is ludicrous. Aside from legitimizing crude ethnic slurs (like insinuating that people of Asian ancestry can't keep their "l"s and "r"s straight), this implies that there is something false or inferior about people learning to speak a language that wasn't spoken in their home growing up. SC thinks this is patronizing and bigoted, especially in light of point 2 above.