The “program” is the package of instructions that tell the machine what to do. The instructions are written in a programming language.
With a markup language, the markup is the input to a program (like a browser) that tells the machine what to do.
But I think it’s not really boolean, it’s a sliding scale. Especially with so many programming languages being interpreted or JIT compiled. I think it’s less a programming language than many other programming-related things, but more of a programming language than, say, a slideshow.