The notion that humans have a genetically determined preference for grammar is an interesting one.  A specific sequence of molecules present in the DNA of every human determines the structure of all man's language, which ultimately influences the way we communicate with each other and perceive the world.  The implications of such a notion are intriguing.  If there's a genetic basis for the structure of language (and reality), then it was shaped by natural selection.  If it was shaped by natural selection, it can be further altered through natural or artificial selection.  Although it would be highly interesting to see what the effects of such selection would be on human populations (entire new ways of seeing the world?) such experiments would have problems with feasibility and ethics.  Maybe, even without direct intervention, such changes have been occurring over the course of human history, gradually changing the way humans interact with each other and the universe at large.  This idea could possibly be tested through some sort of wide analysis of modern texts with more ancient ones (or at least it could in a hundred thousand more years, if we're still around).

 Another interesting area of investigation would be the more rudimentary languages of animals such as whales, who some say have dialects and cultures (http://www.physorg.com/news/2011-12-evidence-sperm-whale-culture.html).  Do whales have common and inherent rules of language, similar to humans?  Do we even share some of these rules?  It would be fascinating to see how far back the structure of human language began to emerge, and what creatures we share this structure with.

A genetically determined skeleton of language also spells bad news for anyone who hopes to make contact alien species at any point.  Ignoring glaring biological differences that are likely to get in the way of any interaction between human and extraterrestrial, and the vast unlikelihood of running across anything with the sort of intelligence needed to communicate with humans, if they had a language it would likely be so fundamentally different from our own that we would have no chance of translating to or from it.