It depends on the type of parody. Your definition seems to stick to literature parody only. If you extend the definition over literature and text, I think it's important to use the same visuals and pretend to be the company or individual ... see also: https://www.adbusters.org/spoofads (they classify for me also as parody and they are spoofs, pretending to be the original source). A parody is often also called spoof, which in this case fits better I think.