It is called ambipolar because it changes its behavior. It acts like a p-channel FET when the gate is at one polarity and an n-channel FET when the gate is at the other. So, it wanders ("ambi", think "amble" or like "ambidextrous") between polarities. What I am curious about is whether there is a dead band between polarities and is that controllable. I would also like to see a couple of simplified schematics using the device.
Life could become really interesting; does ambipolar therefore not need a substrate bias to prevent latchup? Could we discard our old 'nominal 0V' substrate and run everything in true differential? Every signal could have a mirror in the opposite polarity, giving potential for low crosstalk and low supply voltages/signal swings... could also make it easier to recycle charge locally instead of burning it in resistive losses.