Debate: Language or Communication?

I first heard about the whistled language of Gomera from a student in my Introduction to Linguistics course; as soon as class ended, I YouTubed "whistle language" and found this video.



It's a fascinating display.  My question for you is whether the "whistle language" is truly a language or is actually a communication system.  For anyone unfamiliar with the differences between the terms language and communication system, one primary distinction between the two is that humans are said to have language while animals have communication systems.  Animals can communicate specific needs (such as danger, food sources, or mating rituals) but do not have full-fledged languages that allow them to produce new and creative utterances, abstract notions (they can only address the 'here and now'), and pragmatic features like sarcasm or humor.  Language, on the other hand, allows humans to talk about any chosen time period, focus on any person--real or fictional, discuss theory, produce unique utterances that have never been used before but still have meaning, and use intonation and pitch to show emotion in speech.

What do you think?  Is the "whistled language" a communication system?  Or a language?