They are opposites, in that the vessyl site strictly discusses apps and salesmanship without mentioning how it works whereas this project is strictly how it works and what it does and you figure out what to do with it.
I enjoyed reading the vessyl site because it explained nothing at all about how it works, so I immediately applied my engineering gut sense to trying to figure out how I'd make one if I wanted to. Small scale calorimetry heating and cooling with a peltier device a couple degrees at a time? That works for metals and phase transitions but probably not enough to tell diet sodas apart. Some kind of high res ultrasound to analyze waves and thus viscosity and thus density/composition? Personally I'd go all EE on it and shove a modest AC signal thru a big capacitor and get the dielectric constant of the "stuff" in the cup. A really accurate capacitive sensor to tell exact volume with a really accurate force sensor on the base to read weight/mass and a decent thermistor to calibrate for temp and you've got density at a specific temp. Once the raw data is in there, I'm guessing its all just lookups and best fits and the like.
spectruino's ADC isn't fast enough to capture all the data from a CCD data frame, thus to get an entire spectrum one needs to sample multiple times and shift the ADC sample clock... or deal with not having all the pixels. This method would be fine if your samples aren't changing, but for something like enzyme kinetics this non-simultaneous method will likely yield poor results. For applications that can use a monochromator, this method should be fine (albeit with lower spectral resolution since monochromators usually have quite high spectral resolution)
I'm still yet to find an actual use for the thing, regardless of constraints/limitations. The fact is, until we have a use of the hardware which allows average-person to gain some advantage, we have little progress.
[0] https://www.myvessyl.com/