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.
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.
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.
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?