The evidence that they are using a complex "language" is definitely weak. For example, how does it prove that they aren't simply saying, "Hey, hey!" to each other like the Far Side cartoon[0]? I would have preferred more interpretation of the different noises the dolphins make over the fact that they are making them in the first place.
They same way we are almost certain that the Voynich manuscript contains an undeciphered written language, by applying a combination of information theory, computational linguistics, and statistics.
[0] https://pupster.files.wordpress.com/2008/01/dog-translator.j...