This is interesting work, but I don't think it justifies the plain-English summary. If you're going to claim that language is not a tool for thought, I would expect you to demonstrate that a difference in language does not lead to a difference in thought. To answer that, you shouldn't just look at whether language-focused brain regions are activated during non-language-based activity, but also whether a lifetime of using Language A leads to differences outside of those regions compared to a lifetime of using Language B. Isn't that the crux of linguistic relativity? That different languages encourage and train different modes of thought?

Any chess player will tell you that they apply their "chess brain" to all sorts of things outside of chess. It's not that we literally view life as a chessboard, but rather that a lifetime of playing chess has honed a set of mental skills that are broadly applicable. The fundamental logic applies everywhere.

In particular, some deaf children who are born to hearing parents grow up with little or no exposure to language, sometimes for years, because they cannot hear speech and their parents or caregivers do not know sign language. Lack of access to language has harmful consequences for many aspects of cognition, which is to be expected given that language provides a critical source of information for learning about the world. Nevertheless, individuals who experience language deprivation unquestionably exhibit a capacity for complex cognitive function: they can still learn to do mathematics, to engage in relational reasoning, to build causal chains, and to acquire rich and sophisticated knowledge of the world

It seems like they are using a narrower definition of "language" than is appropriate. e.g. I don't think it's controversial to include body language under the umbrella of "language", so I am very skeptical of the claim that any of those deaf children had "no exposure to language".