I would argue that UI/UX Designer might not, but UI/UX Engineer inherently does.
> But if they're looking for someone to program, it should be outlined in the responsibilities.
It was.
> Knowing "HTML/CSS/JS" is different than building an entire application (just an example).
FizzBuzz doesn't test ability to "build an entire application". It tests fairly minimal ability to apply logical reasoning and apply it with a programming language.
If you can't solve FizzBuzz in a programming language, its not unreasonable for a company to see that as a strong negative signal for any job requiring proficiency in the language, and JS proficiency was advertised as a requirement for the job in question.