I'm not an expert but since I seem to be the guilty one here let me answer
What we call "piezo" is basically systems that exploit the piezoelectric effect, where voltage is generated through mechanical stress (pressure) in a piezo crystal. so basically you put this material under the saddle and as the string causes the saddle to vibrate, this gets picked up and translated into alternating current. So this is independent of the sting material, and on the other hand it will pick up things like knocking on the saddles etc.
Its best used with a preamp, the graphtech system has one, they call it the "acousti-phonic", but that's not the only option, I have a Mayones 7-string that has graphtech saddles, but they are using some preamp they designed themselves. The graphtech one lets you mix between the piezo and magnetic pickups (which of course wasnt needed in my case)
The reason the graphtech system has 6 cables is that it doubles as a hexaphonic midi system if you add some additional hardware, so you have separate signal from each string. But thats not necessary in general, typically electroacoustic guitars have a single piezo "pickup" under the saddle with just a pair of wires running to the preamp, and that is probably the case for the one you link.
Back in the 80's my brother had a really cheap acoustic guitar and he bough for next-to-nothing a small "piezo kit" which was a coin-sized thing that you attached with some sort or wax-resembling substance to the soundboard of the guitar, plugged a jack and played. No preamp. The tone was different depending on where on the soundboard you attached the thing.
hope this helps!