This doesn't really seem like "hyperspectral imaging". I think the idea is having a reference colour chart of known emission characteristics and photographing it through a transparent substance gives you an idea of how much that substance attenuates each wavelength.

It's a cool trick if it works, but it seems very finicky and I guess would be limited to transparent/homogeneous liquids?

On top of that it only works in the VIS range, thanks to the filters in front of the camera sensors - and most of the interesting information is in UV or IR. VIS only contains information about a few elements. (see Fraunhofer lines https://en.wikipedia.org/wiki/Fraunhofer_lines)

In theory maybe you could build a version made of inks printed on a reflective mirror? And then you would hold the mirror so it reflected the object into the camera?

But that seems far more difficult. Precisely combining and applying combinations of inks to a mirrored surface sounds like a helluva manufacturing challenge.