The touch grid is made up of two distinct circuit boards, joined by a small ribbon cable.

One is lined with LEDs and projects, from the top and left side of the Kindle's display. and the other is made up of IR receivers (likely phototransistors), and makes up the right and bottom edges of the display.

There's a bit of circuitry on the receiver board, to monitor the breaks in projected light and detect touch:

Neonode zForce NN1001 Single Chip Optical Touch Controller

Texas Instruments MSP430G2 Ultra Low Power Microcontroller