[In response to responder: Actually I think developing complex language with something like this would be relatively easy. With human language we can't just show a series of events with our words, people need to experience the things with us and then we develop common words to describe them again later. With their system of communication it seems that they could describe pretty much anything they'd find notable and also easily abstract things by just making their clicks less specific or by blending a few specific examples as a form of abstraction. Actually I'd bet on blending first, maybe even a literal superposition of all the possibilities or several of them. Also they might be able to communicate by acting things out physically while they are sounding things out. The combination could be pretty powerful for expression.]
I'm still quite skeptical that the dolphins have complex shared language with features like recursion, but it's possible that the storytelling via pictures could get complex... I guess we'll see.
It may be possible, but I can imagine that it would be very very difficult for us to grasp since if this research is verified we'd likely have so little in common linguistically. It strikes me as kind of like "Darmok and Jalad at Tanagra".
[In response to responder: Actually I think developing complex language with something like this would be relatively easy. With human language we can't just show a series of events with our words, people need to experience the things with us and then we develop common words to describe them again later. With their system of communication it seems that they could describe pretty much anything they'd find notable and also easily abstract things by just making their clicks less specific or by blending a few specific examples as a form of abstraction. Actually I'd bet on blending first, maybe even a literal superposition of all the possibilities or several of them. Also they might be able to communicate by acting things out physically while they are sounding things out. The combination could be pretty powerful for expression.]