In computer graphics these are also called “procedural design” (that being slightly more general), or L-systems.
Prusinkiewicz and Lindenmayer (the L in “L-systems” ) had success describing plants and seashells and other CGI-friendly lifeforms as grammars. Lerdahl and Jackendoff applied these ideas to music. Look around for applications to primatology, genetic programming, gene expression, dynamical systems, Barnsley et al and their fractal image compression…
Design grammars are just ordinary grammars (possibly probabilistic ones, but nevertheless…). Unlike classical the usual linguistic use of the word grammar”, though, the emphasis here is not simply on parsing sentences to see if they are valid or not, but rather using grammars to synthesise entirely new sentences/flowers/trees/dungeons.
I should mention that I am interested in this for artistic/creative reasons rather than purely analytic ones, but there are probably uses in both domains.
Where do design grammars come from? One common term is “inverse procedural modeling” which is a design analogue of grammatical inference.