If we define a programming language as a "language designed to communicate instructions to a computer," and then we observe that most "traditional" programming

If we define a programming language as a "language designed to communicate instructions to a computer," and then we observe that most "traditional" programming languages require an intermediary to make the computer "do what the program intends" (such an intermediary being a compiler or a runtime or some other transformation), then one could argue that HTML is a language, and the browser is such intermediary. Therefore, HTML is a programming language, IMHO. It may be "primitive" in the pecking order of programming languages based on some arbitrary definition of sophistication, but it rises above the stated definition.