Since the Wiimote is a new and unfamiliar technology for most of us, I'm assuming that the small screen is used to show how the Wiimote is to be used. In the kiosk picture the small screen appears to display one larger image of an individual using the Wiimote with a smaller inset demonstrating its effect on the game.I think the small screen is there for some online two-player action, that you can actually play online against a person on the Wii kiosk, and see that person on the screen and he can see you too.
So there must be a webcam on that kiosk somewhere.
A functionality that'd be possible at home with Wii and DS.
Similarily, PS3 and PSP could have that functionality also, which would be quite cool.
You could put the DS or PSP beside you on the sofa, and it'd be almost like playing with someone at the same room. If you'd really be prepared to go further, you could buy a doll, rip it's face off and install a DS or PSP in place of the face, and you'd have almost a lifelike gaming companion!
-aldo