Even if you don't follow the first half, it's worth skimming to get to the bottom where the computations predict the colors of chemical compounds with remarkable accuracy. The "Copper (II) aqua ion" one is the most impressive to me – the entire color spectrum is spot on.
It's not really "predicting" the colors, per se. The UV spectra being downloaded contain that information already. The code being demoed here is just a transformation of that data to "perceived" color. It's just a transformation between two equivalent representations, not "prediction" really.
Agreed, not really a prediction, but rather a projection. Still, it surprises me that few people take the trouble to make the connection between the spectra and the perceived colors. Seems like photochemistry and colorimetry don't intersect as often as they ought to...