To me, the defining feature is automation. A "programmable" system is one where smaller actions can be composed into larger ones and saved for invocation later (by name, in response to some event, etc). I don't know much about photoshop, but judging from what people have said, it seems to meet this definition.

I will concede that "programming," in the sense of "I've been programming for the last couple hours" or "He isn't very good at programming" implies the use of a Turing complete language. Photoshop would probably fail here, along with more programmer-y things like writing html.