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From the article: "the unique wisdom of some of these words, that don't have an exact counterpart in the English language". So the claim is precisely that because English doesn't have single-word translations of these German terms, that the German words somehow encode "unique wisdom", which is obviously BS.As for the general claim, not so obviously.
For one, "wisdom" here is not meant as some expert understanding of who we are and what to do in general (the generic sense of wisdom), but as improved insight about a sentiment/situation captured in a specific word, as opposed to a language that can only describe it in many ad-hoc words.
To put it in IT terms, those words avoid an extra pointer interaction to the subject matter. Or having them is like having first class support for something that in English only can be achieved with "design patterns" and extra ceremony (of course there are English words which the German don't have too).
As for specific examples in the article, sure, they might not be the best picks to illustrate the general claim.