I never understood the purpose of languages with unicode operators that can supposedly express a 30 line script in like 2 symbols.

Are they purpose built on the spot for CodeGolf?

Not on the spot, a condition for the answer to be accepted is that the language must exist before the challenge, but yes, many languages exist only just for the purpose of golfing. Mathematica is a legitimate language though, it just is the case that some operations are surprisingly compact.

Like checking if an image is of a goat:

    ImageInstanceQ[x,"caprine animal",RecognitionThreshold->i/100]

https://codegolf.stackexchange.com/a/71680

I doubt Mathematica is built for code golf. Check out Burlesque (which is ASCII).

https://mroman.ch/burlesque/docs/BLSQ.html

If ask for a "histogram" of the data, did I just write a 30 line script as a single word?

Someone should actually post it there and then post the question here...