Here I think that it's important to distinguish between language (a specific system of discrete symbols, organised in a recursive way) from communication (ability to send information from one animal to another). Plenty, plenty animals show non-linguistic communication; including humans. But language itself pretty much exclusive to humans.

What those elephants are showing is one of the requirements for language, the ability to assign discrete and arbitrary symbols to things around them. However it's also missing another key element - the ability to combine those symbols recursively, like they were building blocks of something bigger.

It might be also worth to redo a few intelligence tests with them. If Chomsky is to be taken seriously in this regard (I have my doubts), the primary role of language wouldn't be communication, but to structure and formalise your thoughts; now that we know that they assign symbols to things, perhaps we should be looking on how they handle them.