Ok, so, I was doing some reading. It appears that the wiring, once the voltages are converted to 3.3v for the pi, this device would work with the GPIO of the Pi.
When the zero,cross detector sends a signal to the Pi, the Pi would then send a short multi-millisecond pulse to the triarc. The longer the pulse, the dimmer the lights, the shorter the pulse, the brighter the lights.
Now, perhaps the Pi may not be precise enough with a general Linux distro, but I would like to know if my general understanding of the circuit (or rather circuits, as there are two) is correct.