How do universities deal with the length of assignment submissions (e.g. word count) in pdf?
My only direct experience with this kind of academic word limit has been with my Master's and PhD dissertations. In both cases the official submission was in hard copy. Under those circumstances, I find it vanishingly unlikely that anyone did a word count -- I suspect that at my university, the word-limit rule would only be invoked if someone submits something that's blatantly too long (e.g. a 500-page MSc thesis).

I would guess that other universities deal with the issue of PDF word counts either by not caring much (as in the case of my dissertations), or simply by counting the number of words in the PDF: despite your university's insistence that this is impossible, there are dozens of free tools, both web-based and downloadable, which can accomplish this task. Even without those, Adobe Reader has a "save as text" function which produces an easily word-countable plain text file.

Another possibility is that those universities set the limits in terms of pages, not words.