You do not need to rotate or oscillate the electrode for successful EDM. In fact doing so will reduce accuracy of cut, because the motion will need clearance to work, and that clearance will be multiplied by the distance from electrode tip to rotate / oscillate mechanism , cutting the hole much larger than the electrode.
An accurate linear slide to hold the electrode, and a DC gearhead motor or servo to operate a leadscrew to drive the slide up and down are all that is needed, if you use the Ben Fleming design. If you are going to spend some cash, get a decent linear slide and forget about rotating the electrode with the apparatus in your picture.
I built a Ben Fleming Mk.1 conventional EDM (sink) machine in 2009-2011 with such a slide (from Deltron in the USA) and some other variations and it has worked great since. If I make copper electrodes .003" smaller than the desired finished hole dimension the holes (whatever shape) come out VERY close to dead nuts on size.