Apparently Philips already made a commercial version of these:http://www.research.philips.com/newscenter/archive/2006/060104-entertaible.html
..kinda weird since i read somewhere that apple is holding the patent for that technology. well.. competition makes it cheap hopefully.
ambient light does not seem to be a problem, they might have used some simple infrared filter on the screens surface to keep unwanted infrared interferences outside:
"While the concept of a multi-user digital table is not new, previous solutions have utilized complex arrangements of overhead cameras and dimmed lighting that detract from the user experience. The Philips Entertaible, however, is based on a series of infrared LEDs and photodiodes discretely mounted around the perimeter of an LCD screen. It requires no special lighting conditions or other equipment and is entirely 'hand' operated by touch alone. Entertaible can simultaneously detect dozens of objects, including fingers. "
..it would be nice to know whether it is possible to build that thing at home with no superbig effort