As far as I tell (it's not my story after all), the author appears to be asserting that Inuktitut is somehow uniquely in tune with nature in general (dubious) and that we could change the way the Western world acts by absorbing some of those words (which sounds like linguistic determinism to me, not to mention even more dubious).
As for Turing completeness, my off the cuff analogy is that just like any Turing-complete programming language can implement any algorithm, any natural language can state any expressible human thought.