To communicate explicitly on the football pitch, you use a combination of names, pronouns, short phrases, hand gestures, head movements, etc. But actually most of the communication on the pitch is implicit--players observing each other, inferring the mental state of each other, and making changes based on those inferences. That's how players running at full speed are able to improvise complex plays involving long passes.
This is how I think of the communication between smart social animals like wolves or dolphins. They are like a football team. Every individual is an athlete, with essentially similar physical characteristics and skills. And they interact to accomplish essentially athletic goals, like hunting, or asserting dominance, or mating.
So, I'm not holding out hope that dolphins have a secret rich language, or even an interest in developing one. Heck, even among humans, professional athletes do not have a strong reputation as deep thinkers. But they think a lot about their particular sport.
The movie Avatar, while terrible overall, got this right, I think. Scientists failed utterly to make a connection with the big blue natives. It wasn't until a warrior (by accident) took on the task that the connection was made. The big blue natives were themselves warriors, so of course that is the type of communication they valued most.
Edit just for fun:
http://www.dailymotion.com/video/xqrzuj_the-life-aquatic-wit...