Yes. Markup-Languages are a subset of Programming-Languages. Turing completness doesn’t matter as things like magic the gathering and habbo hotel are Turing complete
ACKSHUALLY ... markup languages do not produce a formatted document. They define semantic elements of the document. The formatting is done by the compiler (whatever it is in the individual context) based on styles defined by a styling language.
'This markup language isn't even as capable as Habbo Hotel, but it counts anyway because I just called it a programming language.'
There is a literal hierarchy of syntaxes which are recognized by different categories of machine. Programs require a Turing machine. Anything lesser - in a subset like pushdown automata or finite-state machines - doesn't need a proper computer. So it's not a program.
Can you just drop to assembly for what you want to do?
Gnu compilers even have inline assembly, but with any compiler you should at least be able to built a separate, assembly, object file.
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.
Does HTML or LaTeX or Markdown provide a computer instructions which are executed? I'm going to take the unpopular opinion and say they are programming languages.
As much as a lot of us dislike it... I think it is difficult to argue for e.g. python being a programming language without including html in it.
And honestly if python is no a programming language because you use an interpreter... Then I would love to hear a non-bad-faith argument for c being a programming language as e.g. GCC could easily be viewed as an interpreter too. Obviously there is a difference but is that difference really the difference that you want it to be?