A 1-1 mapping isn't required, IMHO everybody involved would consider a probability distribution as a reasonable expected output, and as long as that probability distribution is reasonably close to reality and is substantially different from the prior, output like that is useful signal and would count as the system working.
The same applies for labeling, if a particular facial expression can occur in an indistinguishable manner because of three different causes, that's okay; there's nothing wrong with a gold standard label in training data marked as "we've observed that 50% people had this expression because they were angry and 30% because they were in pain, but no happy or sleepy people had an expression like that".
Furthermore, for the purpose listed in the article, you don't need to determine an absolute value of some emotional state, but you need to detect large shifts in it (i.e. you get an baseline that implicitly adjusts for part of individual and cultural differences) - i.e. whether the audience (in aggregate!) now looks significantly more frustrated than the same people looked 30 minutes ago.