Word specifically is not required, but electronic hand in is. If it works the same as when I studied at that level (I am a Dane) you simply hand in a pdf file, but how it is made doesn’t matter. A web interface to write in was never a thing throughout my education though.
While I agree with you that LaTeX is an impressive tool, I would not choose it for an exam whith a short duration. It is great, but for short documents that should be written quickly, I don’t think it’s the best tool.
A single person experiencing an error is bad luck and may go through an apeals process. Half a class experiencing the same error jeopardizes the legitimacy of the exam for enough students that they decided to handle it collectively. It may be a third party tool but it is one they are expected to use which changes things. Had it been a few students using libre office they would probably be out of luck as they would have used non standard software.
Another important note is that many exams now require digitally handing in the assignment, so the only alternative to writing the assignment in a text editor would likely have been to scan a handwritten one and convert it to pdf, if that was even allowed. So while particular hardware and software isn’t required, the limitations of the exam makes it impossible to completly avoid errors such as these.
Just a note to avoid some confusion some people may have: gymnasium in denmark is roughly the same as high schools in the US. While I’m sure the problem also affects university students, the focus of this article is on the high school students specifically.
I’ve used it a lot for reports when I went to university, but for short notes I would prefer markdown and for a few pages or documents where formatting is trivial I still find it easier to use LibreOffice or word. I find it likely that most high schoolers would find it easier to use word for any document than LaTeX which they probably have never heard of and would be unable to get support for unlike word which is commonly provided by the school. So while understand where you are coming from, I don’t think the students are in a situation where that would be a plausible solution. Especially due to the many pitfalls and the learning curve you have to get through for using LaTeX as efficiently and for as complex formatting as they already know how to do in word. LaTeX has a way higher ceiling of quality, but the floor is also much lower for those new to it and without the drive to learn it.