I take the article to be endorsing the following principle (P): "all beliefs should make an empirical prediction". However, I'm not convinced. Here's why:

1. The conclusion seems self-defeating. What empirical prediction does the belief "all beliefs should make an empirical prediction" make?
2. Ethical counterexamples. Ethical beliefs like "we should save more lives rather than fewer" does not make any empirical prediction, yet (and I think the EA community would agree) it is a legitimate belief.
3. Lack of motivation: P seems to be motivated by the rejection of the professor's "retropositional author" beliefs and the alchemists "phIogiston" beliefs. However, I do not think we need to endorse P to claim that these beliefs are poor. Instead, we can claim that the professor's belief is poor because it does not do one of the things a good definition should: explain unknown concepts in terms of known ones. Additionally, the alchemists belief is poor because we now have better explanations of how fire works. 

If I've interpreted the principles of the article uncharitably, or any of my critiques are mistaken, please let me know. I'm interested so see what others think.