Turing completeness is a separate axis. There are programming languages that are famously not Turing-complete (for guaranteed halting) and there are (actually, surprisingly many) “things” that are Turing complete, but are not programming languages at all. The latter includes Game of Life, many boardgames and PowerPoint.

As most human things, programming languages don’t have a specific definition, but as a point of reference we should probably have a look at whether that “thing” was ever intended to be used as that. Sure, there is a program that can encode loops into html tags, but it is generally used as a markup language for describing the DOM. Not for programming it.