The demo appears to be running within the iPhone SDK simulator. We've previously posted screenshots of the iPhone 2.0 Japanese keyboards. Tokyo Mango describes the input method:
You can pick from a muti-tab style kana keyboard or a sliding keyboard. Japanese kana letters are organized in groups of five according to a beginning letter and corresponding vowels (a i u e o), so you can either put in the first letter and then hit the same key b/w 1-5 times to get the right sound, or you can put the first letter in and then scroll through to see all five sounds and pick the right one.