>language is far from arbitrary labels for things

I think this is a misunderstanding of the arbitrariness of the sign. Arbitrary doesn't mean "random" or "uniformly sampled." The fact there are systematic tendencies among languages in how things are called doesn't negate the arbitrariness of the sign, they could have been called other things. We can also decide to refer to things by another name and we can use any arbitrary name we like! There is no limits on what names we can use (besides silly physiological constraints like having a word with 50 000 consonants). But, of course, there's much more to language than just labels!

For me, the interesting thing in this paper vis-à-vis language is that it shows how much innate structure in cognition must shape our language.