While it is literally true that the CW-80 and other voltage controllers, like dimmers for incandescent lamps, "chop" the waveform, that term usually would imply a rapid switching on and off, so that the average output voltage over a time short compared to the power-line cycle is proportional to the chopping duty cycle. The use of a fairly simple low-pass filter can do that averaging, resulting in very little distortion of the original sinusoidal waveform.
But what the CW-80 does is different, and it is usually called "phase control". The switching occurs just once in each half cycle, which results in a very mutilated waveform that would be impractical to clean up. It works satisfactorily for incandescent lamps, which respond very sluggishly to their input voltage and thus provide a sort of thermal averaging, but can be problematical for more complicated electronic loads like compact-fluorescent or LED lights--or modern toy trains.