"How are the LED's detected?"
The title of the paper is:
Low-cost multi-touch sensing through frustrated total internal reflection
My guess?
Shine light thru the edge of the plastic. Where you touch will create a loss path for the light (think of a glass of water - reflective until you touch the side of the glass, at which point you can see your fingertips) and the system is able to interpret the intensity changes as a position.
See? You're not the only geek...