Nah, not really. You can consider the term “programming language” to refer only to those languages capable of computation, but then you’d have to include LaTeX and CSS3, because they’re both Turing-complete. Where do you draw the line?
Probably the most reasonable way to cut it up is to treat programming, markup, and styling languages as subsets of computer languages. They all overlap to varying degrees, and Turing-completeness is entirely separate—Magic: The Gathering is Turing-complete, and nobody is calling that a computer language of any kind.
I guess it depends on what type of person you are, what type of rules you use to distinguish things. So I am always looking for isomorphisms and equivalence relations. So to me if you are Turing complete then I can define an equivalence between you and a programming language. So Html5+css3 goes in. You can encode turing complete computations into Magic the Gathering? Then yes MTG + Appropriate Encoding can be talked about in the same sentence as programming language.
Whether or not these languages can also be found in the Turing tarpit is a separate thing.
The point isn't that your rules are a bad way of defining computation. The point is that your rules are basically irrelevant as far as deciding what an acceptable language for an online course would be.
Markup languages, even ones that are utterly incapable of encoding even a trivial computation, are way more relevant to computer literacy than Magic: The Gathering. I can guarantee you a beginner will learn more if I teach them how a computer interprets Markdown or HTML than if I teach them how any general computation can be embedded in a card game.
I for one am with you. We were only talking about reasonable ways to divvy up the different categories of language, which is only tangentially related to the article.
Probably the most reasonable way to cut it up is to treat programming, markup, and styling languages as subsets of computer languages. They all overlap to varying degrees, and Turing-completeness is entirely separate—Magic: The Gathering is Turing-complete, and nobody is calling that a computer language of any kind.