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]
Where you put it is not my problem.
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:
Programming language
Sometimes even non Turing complete languages are considered a programming language but Turing completeness usually is the criteria agreed upon: