In which way is he vague? He basically reinvented a Turing Machine with human language and brought linguistics around to the idea that, yes, language isn't something that's vaguely "out there" tabula-rasa-style, it's built into our genetics at a very fundamental level. Fundamental enough that he tied linguistics DIRECTLY to math and from there to programming. The Chomsky Heirarchy is no joke.
Your link relating to statistical models is only a tiny, tiny part of Chomsky's fundamental arguments and even then is debatable.
> it's built into our genetics at a very fundamental level.
Chomsky's evidence for this is.... iffy at best. Yes, I think we are predisposed to HAVE language, but I don't think we can learn as much as he proposes about the structure of modern language from the human genome.
2) I don't think the problem with learning about language from the genome is specific to language. There are just so many layers of molecular interactions between the genetic code and activity at our level of reality that trying to link the two is incredibly difficult, and we are not even close to having the computing power or theoretical models necessary to link them up. But that doesn't mean that language and genes aren't linked.
Being cited doesn't mean he has something specific to say about those fields. He's an influential scientist so people may cite him when they found something vaguely related to his theories, to make their findings seem more important.
I didn't imply a yearning for anything, I was just saying a citation can mean different things in different circumstances. I think you've fallen prey to the polarization that Chomsky is putting forth: either you are dealing with huge amounts of data and don't care about theory, or you're a rationalist whose theories don't need any empirical support. The reality of successful science is on neither of these extremes, of course.
And by the way I do think that judging human performance by simple metrics is problematic, but not because it's statistics or not 'high-level', simply because it doesn't take enough information into account; it's a shortcut to the actual concept of quality, which is dangerous when metrics are used in decision-making. Automated metrics give an air of objectivity which an expert opinion doesn't have, even though the latter may well be much more informed.
Your link relating to statistical models is only a tiny, tiny part of Chomsky's fundamental arguments and even then is debatable.