Now, from what I've learned/read about their behaviours, I have no doubt on the depth of their lives. https://en.wikipedia.org/wiki/Elephant_cognition#Elephant_so...
And I wouldn't call that "some sort of language". That's language. Species-specific. Not "human" language.
Even language that another species can grasp more or less perfectly. You can get that with minimal observation of dogs, cats, even birds. And obviously, animals read us as well.
Now, the complexity of an other species language may be partially out of reach because we do not have the same senses, abilities, history, memories.
So they might even engage in activities we cannot grasp or identify (and reciprocally) but for great patience, observation, study, understanding, and luck.