The paper "Digital genres: a challenge to traditional genre theory" by Askehave and Nielsen (2005, vol. 18, N 2, Information Technology and People) argues that the Swalesian genre theory must be revisited to incorporate medium into it. According to Swales, genres are characterized by three components: communicative purpose, move structure, and rhetorical strategies.
The authors argue that media properties, specifically multi-medianess (text, sound, animations) and hypertext/hyper-reading (non-linear content and reading patterns facilitated by links), must become part of the model. They examine homepage as a new web-mediated genre. The revised genre model includes two modes, reading and navigation. In the reading mode, the text must be characterized in terms of communicative purpose, moves, and rhetorical strategies. In the navigating mode, the medium must be characterized in terms of its communicative purpose, links, and rhetorical strategies.
While I agree that medium is an important characteristic that influences text production and communication, I think it was important before the web as well. Whether a text is printed (as a book or an article) or recorded (using analog devices), it will affect its content, perception, and use. And print media also have a navigation mode (table of content, page numbers, indexes, cross-references, etc.). So what is different? Something is different, since we didn't pay much attention to the medium before or considered it to be a transparent element of the genre. Perhaps, it's speed, immediacy, increased quantities of information, etc. brought by digital media that affect text production and consumption in digital genres.