Can "beamer" mean "projector"?
Solution 1:
"Beamer" is in use by native German speakers, including in English (a German dictionary translates it as projector). In speech this pseudo-English word is common, probably more so than the more formal "Videoprojektor". As projectors have long been in use in academia and most German academics can and regularly do speak good or excellent English, a slight misuse of an English word (false friend) can persist in this sector (and related ones - German engineers use the same false friend in English). Colleagues can easily pick up on the term if they're unfamiliar with an alternative (and new graduates in particular haven't often need a term for the box that puts the picture on the screen).
So it's an error, but a comprehensible one, especially where there are Germans around, such as in UK universities. The LaTeX package beamer was started by a German; its existence probably helps propagate the usage.
Solution 2:
The article "What Is Difference Between a Beamer & a Multimedia Projector?" by Sarah Clark explains it.
It states:
"Beamer" is a word used in European countries that is synonymous with "projector." A European beamer has the same standard equipment and serves the same purposes as an American [multimedia] projector.
It also states:
There is no difference between a beamer and a multimedia projector, except for their names. Of course, there are differences between the functions and capabilities of all projectors, but those differences are determined by brand and style.
So, the word beamer is European English and refers specifically to a multimedia projector, not just any projector. Americans probably won't know what you mean if you use "beamer" to mean that unless you're standing right in front of one and are pointing at it while calling it that.
Actually, the word I use and everyone I've heard use, like at the high school 🏫 (American ) where I work, is "proxima," which I think came from a name brand, kind of like "kleenex." I say "proxima" to mean a projector that hooks up to a computer as opposed to saying "projector" because "projector" is taken as meaning a film projector, so if I ask the A/V Department to bring me a "projector" third period, they'll bring me a film projector 📽️. I have to ask for a "proxima" if I want them to bring me a multimedia projector. But maybe that's just where I am, jargon at my work, because it's not like I talk about this stuff outside of work to know what other people call it. I wonder what they'd do if I asked them for a "beamer"?😉