“hill climbing” is a bad term for this since it definitely means something to computer science folks.
This is a good, albeit general, article and I really enjoyed and tracks with my experience putting models into production. But I didn't read it at first because I assumed it was about, as you point out, the specific mathematical/data science concept of hill climbing. The final paragraph buries the lede that the company decided on this term to refer to it's internal process and has nothing to do with the data science concept.