The only mention of chess960 is on the navigation bar at the top of the page, which leads offsite and which doesn't appear to have been updated in two years. If you're patient, the clock will eventually appear in one of the blurbs that rotate through 'DGT Headlines'. There's also an unlabelled picture of the DGT960 (Hint: It's a folding clock with orange as a dominant color) that leads to the main page on the product: DGT960.
These days I suppose that being found in the search engines is more important than internal site navigation, and Google reveals several other interesting pages on the DGT site. First, there is a collection of the same YouTube videos I flagged in my original post on the DGT960: How to operate the DGT960. Then there is the product's user manual: DGT960 User Manual (English). Finally, a page announcing The NEW Chess960 Ambassadors! ('Miss Bianca Muhren and Mr Dennis de Vreugt are the new Chess960 Ambassadors') leads to the same chess960 offsite page I mentioned earlier: DGT Chess960!.
Disclaimer: While I haven't used the DGT960 myself, I have used and written reviews on other DGT products: Two Digital Clocks from DGT and Review of the DGT 2010 Digital Chess Clock. They were all top quality clocks. I can't imagine buying the DGT960 solely for the chess960 functions, but I will definitely consider it if I ever buy a new chess clock.