Judging by the touch switches and display there is evidently a lot of digital electronics inside the box. Pitch-shifters and harmonisers generally quantise the source signal using either BBD (Bucket-brigade devices) and some digital clocking or a combination of ADCs DACS and digital memory and some similar digital clocking. 

 

It could be argued that none of these are purely analogue in that sense because the input is cut-up into slices and then slowed down or sped up to create the change in pitch (and then mixed with the source to create harmony) and the master clocking, even if derived from the source using phase-locked loops or some other form of frequency synthesis, is a digital signal. Certainly BBD is a time-domain sampling methodology and suffers all the failings of sampling theory, so going digital in this application is not a major hurdle, and in many ways is the better solution.

 

Both versions will have some analogue noise (hum, buzz etc) associated with them because there is an analogue path through the device and a lot of digital switching involved, given the current state of ADCs and DACs personally I find it unlikely that anyone could honestly tell whether it used a BBD or a ADC/memory/DAC method just by listening to it. Yet I'm sure some analogue purists would argue until they are blue in the face that they can

 

However, BBDs fell out of favour relatively quickly so very few commercial units used them, though they are still popular with some home-build enthusiasts (if you can find stocks of them, I believe only one manufacturer is still producing them).