As mentioned, HTML is indeed a programming language. But it’s one that is rarely used on its own. So you could argue that having it as a thing of itself in these lists, makes little sense.
If it’s a programming language, so is Markdown. (It’s not, either.)
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I believe a reasonable way to categorize languages as programming or not is simply.. what is it's primary use case. HTML's last two letters tell us exactly that it is not a programming language.
The reason this debate is so strange is because some people think it's gatekeeping to say someone who writes html for a living isn't "programming". It's nonsense.