I have been mulling over config files and their relationship to code for a while now and depending on the day and direction of the wind my opinions seem to change. More and mor
You could turn to theory of computation to define what counts as a programming language. If your configuration file format is Turing Complete then it reasonably counts as a programming language. By this definition, a file format to describe levels of Sokoban counts as a programming language (see here). There are other levels of complexity below Turing Complete that may also count, such as Regular Grammars and Pushdown Automata.
Another way to look at it is that many config files are only capable of data markup, whereas a proper programming language must be able to implement algorithms. For example, JSON is a config file format, whereas ECMA Script is a programming language.