I can't imagine there are more possible diagnoses than there are fictional characters and famous people.
The decision algorithm in the article is amazing in its accuracy and simplicity. There is probably some other low-hanging fruit in reproducing this method in other areas of medicine by working with someone who already has a high degree of accuracy in their diagnoses, but doesn't fully understand their own process. But outside of areas where anyone has the current ability to make such accurate diagnoses, it would be a lot more complicated.
You'd need to determine which factors are important, which of those are covariant, and how that relationship works. Then from there, work over tons of data to establish a bayesian model with weightings to apply to each factor so that you can observe the evidence, plug it into the model, and get out your probability distribution over possible diagnoses. It's no easy task, but I believe that this kind of approach is the future of medicine.
BTW. try to make it guess itself ;).
The game report is interesting: http://imgur.com/5YRk8jv