The general census is that latex actually is an example of programming languages sharing semantics with non programming languages and not being intend as a programming language.
since you linked to wikipedia:
The domain of the language is also worth consideration. Markup languages like XML, HTML, or troff, which define structured data, are not usually considered programming languages.[12][13][14] Programming languages may, however, share the syntax with markup languages if a computational semantics is defined. XSLT, for example, is a Turing complete language entirely using XML syntax.[15][16][17] Moreover, LaTeX, which is mostly used for structuring documents, also contains a Turing complete subset.[18][19]
Sometimes even non Turing complete languages are considered a programming language but Turing completeness usually is the criteria agreed upon:
The majority of practical programming languages are Turing complete,[5] and all Turing complete languages can implement the same set of algorithms. ANSI/ISO SQL-92 and Charity are examples of languages that are not Turing complete, yet are often called programming languages.[6][7] However, some authors restrict the term “programming language” to Turing complete languages.[1][8]