It's really just acting like a switch. I'd hazard to say you could call it a class 'D' amplifier, but even that would not be right. Class 'C' would, I guess, be closest.
Edit: On second thought, no, it's not a class 'C'. It's just a switch. It gets driven between saturation and cut-off and is not linear in any way. For lack of a proper name, we could call it a class 'S' amplifier.