It's typesetting DSL, but if you want to typeset you'd need a typesetting meta-DSL. The one thing that works fine with TeX is math, because math typesetting is build in. Typesetting something more specific other than english text and math is hard and ugly.
If does follow imperative paradigms, as it does, the programming language part is essential if you want to do anything meaningful with it. If exotic task you never need in typesetting, such as multiplication, is hard to implement, something is wrong. And IMO that is why LaTeX is so odd and hackish.
Context is much better, tough.
And, by the way, the unfortunalty dead ANT uses a nice Haskell like language and is still a typesetting DSL.
rather than "TeX is not intended to be a programming language." It is nit-picking to be sure, but I think that, if the creator of a language (especially one who knows his stuff as Knuth does) says that it is a programming language, then it is.
In summary, TeX is a special-purpose programming language that is the centerpiece of a typesetting system that produces publication quality mathematics (and surrounding text), available to and usable by individuals.
(P.S. To "so, is XSLT a programming language because of, say, http://www.unidex.com/turing/utm.htm ?" I say "sure, why not?" What is the point of excluding something from being a programming language?)
Actually LaTeX was invented to be a typesetting DSL. As someone who has taught TeX and LaTeX and written my own software on top of TeX, I have come across this question very often. Basic TeX is not meant to be high level at all. LaTeX hides the complexity of 95% of the typesetting needs.
