There are three dialects Wookies can speak, Shyriiwook, Thykarann and Xaczik. However Chewbacca speaks only Shyriiwook.
From Star Wars news article,
You may think the Wookiee language can’t be too complicated. A howl here, a gruff there. But the reality is there are actually three different languages spoken by the species, all consisting of the same growly howling format. Chewbacca speaks a dialect called Shyriiwook, while other Wookiees may speak either Thykarann or Xaczik. Shyriiwook is the most common to understand, however, as both Han Solo and Rey can decipher Chewie’s grunts.
Now coming to your question,
Does the Wookie language have actual vocabulary and syntax?
Yes. In fact, it has. From the same article,
Fun fact: Wookiees have 150 words for “wood” but no word for “artist.” They see their amazing carving abilities as a survival skill, not a talent.
Since it mentions words, it means they have vocabulary.
A few words taken from Star Wars: Absolutely Everything You Need to Know(Wikia link to the book with the same name),
How to speak Shyriiwook
"WYAAAAAA!" = "Hello!"
"AARRR WGH GGWAH" = "Jump to hyperspace"
"ROOOARRGH UR ROO" = "I have a bad feeling about this"
"WWWAH RRROOOAAAH WHA?" = "Want to play some holo-chess?"