The idea that any language lacks recursion is firstly very poorly supported — the only person who actually thinks this is true and demonstrated by any real language is Daniel Everett who thinks Pirahã lacks recursion, but there's a wealth of argumentation over whether this is true or not (for starters see Nevins, Pesetsky, and Rodrigues's "Piraha Exceptionality: a Reassessment" for a good discussion on this). Secondly, it's not crucial to any contemporary, wide-spread notions of Universal Grammar that languages have recursion in their structure — the theory of Syntactic Structures does not suppose, or even depend upon, expressions having recursive tree structures, it merely hypothesizes that the grammatical processes of a language can only employ structural relationships (and syntactic types) to determine when they can or cannot apply, but this idea has long since fallen into the dustbin of history as ever more non-structural phenomena (features, binding, etc.) became relevant to the grammatical theory.

Second, there has yet to be a demonstration from any known language that the language actually does not have an underlying tree structure to it — even the most free word-order languages such as Warlpiri display evidence of tree structure. NLP people may have a major bone to pick with core Chomskyan theory because of the incredibly difficult in parsing using it, but Chomskyan linguistics isn't about designing computationally efficient means of parsing sentences, it's about developing a good scientific theory about the nature of the constraints on human grammars. And I say core Chomskyan theory above because NLP people actually love various less core Chomskyan theory (Head-driven Phrase Structure Grammar, for instance, which has plenty of work done on it in the parsing world; or Combinatory Categorial Grammar which has been looked at quite a lot in the computational literature). The fact that NLP people prefer other methods such as dependency grammars doesn't say anything about the theoretical framework Chomsky introduced any more than their preference for numerical methods of differentiation and integration in mathematics bears on the theoretical importance or validity of precise symbolic differentiation and integration. Or to rephrase that more concisely — just because your computer isn't powerful enough to calculate these equations doesn't make the equations wrong.

I don't know whether or not Chomsky should be #1 on this list, but I do know that you have no clue what you're talking about with regards to contemporary linguistic theory.