Language is not essential for the cognitive processes that underlie thought

>You can ask whether people who have these severe language impairments can perform tasks that require thinking. You can ask them to solve some math problems or to perform a social reasoning test, and all of the instructions, of course, have to be nonverbal because they can’t understand linguistic information anymore. Scientists have a lot of experience working with populations that don’t have language—studying preverbal infants or studying nonhuman animal species. So it’s definitely possible to convey instructions in a way that’s nonverbal. And the key finding from this line of work is that there are people with severe language impairments who nonetheless seem totally fine on all cognitive tasks that we’ve tested them on so far.

They should start with what is their definition of language. To me it's any mean you can use to communicate some information to someone else and they generally get a correct inference of what kind of representations and responses are expected is the definition of a language. Whether it's uttered words, a series of gestures, subtle pheromones or a slap in your face, that's all languages.

For the same reason I find extremely odd that the hypothesis that animals don't have any form of language is even considered as a serious claim in introduction.

Anyone can prove anything and its contrary about language if the term is given whatever meaning is needed for premises to match with the conclusion.

Just as a data point, my guess is that a very small minority of English-language speakers would define the term as broadly as you do, at least in a context relating the concept to analytical thought processes. At the very least, I think most people expect that language is used actively, such that pheromones wouldn’t fall within the definition. (And actually, that’s reflected when you say language is a means “you can use”.) Likewise, a slap in the face certainly can be interpreted, but slapping doesn’t seem like a means of communicating in general—because a slap only communicates one thing.