TOS has such episodes.
Yonadans in "For the World Is Hollow and I Have Touched the Sky" s3e8.
To a lesser extent the people on Beta III in "The Return of the Archons" s1e21. They don't know how to work the technology, but they fear more than worship Landru.
Maybe the people on Gamma Trianguli VI in "The Apple" s2e5, although I don't remember whether or not they were descendants who lost knowledge of technology and just started worshiping Vaal.
When I first saw this episode of TNG, I thought that such a language was impossible. Without even thinking about how often I hear and use phrases that likely make zero sense to someone who doesn't know the same context as myself. Like dealing with someone who lies all too often, "they are the boy who cried wolf" gets used. Meaning, one of these days they are going to tell the truth but no one will believe them. Or saying, "we need to touch base" to someone who isn't familiar with baseball. Sometimes I understand the meaning of a phrase, like "the proof is in the pudding," without knowing what that phrase originally meant. I still wonder what pudding? every time I hear it. So, yes. I can believe the Tamarian language. Because context is important.
I don't think the Tamarian language as a whole is represented in the episode. I can't imagine "Temba, his arms wide"-ing a way to warp capabilities. I think of the Tamarian language shown as a universal shorthand for the Tamarians. Like their society has different languages, but the Tamarian we hear is the common language. That Tamarians specializing in a field of study have their own words and phrases, much like on Earth of today. For example, if I listen to a lecture on biochemistry, I wouldn't understand most of it because I don't speak (understand) biochemistry. I have no context.
I think the Tamarian language is fascinating, and possible.
That was such a bad situation. The whole, "how dare you question me, get out," loss of Gates McFadden. Dr. Pulaski's introduction as Bones 2.0 instead of as a distinct, unique character, and her first comments to Data. I think Diana Muldaur is very talented and a Star Trek icon -- TOS and TNG. Pulaski is a strong character, but that first impression was hard for me to shake. I was happy when Dr. Crusher returned, but by then I was also also sad to see Dr. Pulaski go. I wish that PIC had made room for a Dr. Pulaski appearance.
"We have always believed that The Wrath of Khan is the fulcrum movie upon which Star Trek turned."
I think that this cannot be overstated. TMP did not get the reception, recognition, and bucket loads of money, the studio was banking on. It no doubt took a lot of work, and luck, to get the studio to back a second Star Trek film, even with its much lower budget. There are many reasons we have the current choices of Star Trek series and movies, but I don't underestimate how vital TWoK's success is with the situation. This sounds like a fascinating book, and is definitely on my "I want" list.