Hyper Text Markup Language
A. Yes it's a language.
B. People who write HTML have been called Programmers for decades.
C. Are you writing in a kind of pseudo code that the computer is going to transform into another form? Yes.
I think the problem here isn't that HTML isn't a programming language. The problem is that we don't further classify programming languages.
There should be Platform Languages and Client languages.
HTML is most definitely a Client Language.