I've reinstalled the game recently, and in the main menu a tooltip popped up saying that Dusk has a bunch of cool visual options and whatnot, so I figured it's about the HD and Cardboard visual settings, but when I went into the graphics sub-menu, the only special visual options were for colour-filters.

So how do I activate HD or Cardboard?

For DUSK HD download that ZIP file from the games extras and then extract all the files into a new Dusk HD folder.
Then put that Dusk HD folder into your main game folder. Before launching the game via the Dusk.exe inside the Dusk HD folder create also a config folder inside Dusk HD so that the game will launch with the correct language (English). The config folder is important so that the game can create proper config files for DUSK HD.

Haven't tried Cardboard DUSK yet so no idea how to make that one work.