The grammar was hashed out by the Traveller Language Development List back in 1998, and was honed a bit more through 1999. I contributed very little -- I incorporated a suggested pitch-accent system, and I reworked the verb prefixes; both were done to account for the "three languages" mentioned in Vilani & Vargr.
The lexicon, as well as some hints for the grammar, was started from the Vilani words found in canon CT and MT sources. The grammar itself was devised by a linguist student, who wanted it to have the characteristics of a real human language, and not be noticeably European, Asian, African, Amerind, or what-have-you. Vilani grammar seems to have some affinity with Dyirbal or Finnish (I think). The wordlist has (or had) borrowings from Sumerian and Anglic, though for the most part the words are unique to Vilani.
In particular, Rob Day contributed a bunch of Vilani words back in 1998.
In short, this is a work of many dedicated Traveller fans. I am little more than a compiler, bringing the elements together and trying to polish the rough edges.
By the way, the lexicon is more or less beta-complete, with around 5700 entries. There are a few hundred more words that probably ought to be added sometime in the future, but I'm not up to the task at the moment.