The images on the first link look like they're using Diaper Genie refills. Basically a long tubular bag that gets twisted in sections each time you use it (as Matt described).

The animation in the second link doesn't show how the internal bag mechanism actually works. This is definitely inspired by diaper pails, but it's also got a nice receptacle for the shovel and likely the opening is better suited for shovel use as opposed to dropping a tightly wrapped diaper.

You could always wrap the cat shit in shiny foil paper, stick the pieces into a heart-shaped candy box and send the package to someone you don't like. At least that's how the story my grandmother told me went...