It is all about definitions. Writing instructions for llms is a new activity and we can call it as we wish - but I like to think about it as a new type of programming language instead of thinking about it as something completely new, because many analogies do transfer and you can use them to reason about larger systems composed of prompts. It is after all a way to instruct a machine.
There are differences and the article highlights some of them - but there are difference between programming in a functional language and an imperative one, there are differences between programming for a RISC machine and a CISC machine, there a lots of different semantics that programming languages support. Now we have a language with underspecified semantics.
It is something completely new and we should be thinking about it as such. Analogies can help us here, and I think the analogy of "instructing a software team" is a much more useful analogy than "instructing a compiler" and the latter clouds our thinking.