I disagree.

All photos have an exposure time; that's an inherent property of them (think film). Compositing images digitally on top one another is not an inherent property of photos.

You can double expose film, and I think that's a finer line, but I think the distinction most people care about is really analog vs digital.

That doesn't make any sense. Did you mean double exposures?

Isn't a long exposure one where you leave the aperture open for a long time, but it still constitutes as a single take?

Yes

Even multiple exposures of one frame of film is, as far as I can tell, still generally considered one photograph.