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?)