Is a professional doctorate beneficial for someone looking for a career as a programmer in industry?
You might get different answers for different countries. This answer is for the US.

Speaking as a person who has hired many programmers (both for my own company and for other companies) I feel quite confident that having a doctorate of any kind will not help you land a job as a programmer. The simple fact is, people care about what you can produce. What frameworks, models, patterns, languages, etc. are you effective in? This is what people generally care about from a technical perspective. They will care about other things like how committed you are, how many hours you can work, etc. but what you would gain from a doctorate will not be of value to people who hire in industry.

That said, it can be useful for career mobility. For example, I have see people chose one person over another for an IT management position because one had a doctorate. That turned out to be a terrible choice for the company, but I don't think the problems were connected to his doctorate (he simply had no experience managing people). Some people might see the value in the doctorate but only at a higher level (not entry level).