Oscillates the same way a spark gap Tesla coil does except it uses zener diodes to switch on and off rather than a loud spark gap. Since zener diodes have a much lower break down voltage than air, this allows you to run the circuit at much lower voltage than a spark gap would need. It’s basically just a continuous LC oscillator
You have to wait a few seconds but if you look closely you can see the peak voltage oscillations decreasing a bit, but then inscreasing again. This is similar to the output waveform of a spark gap Tesla coil which is square wave pulses of the LC oscillations. I assume this one looks a bit different because of the behaviors of zener diodes but overall the waveform acts pretty similar to that of a spark gap Tesla coil.
Before I thought the circuit was glitching out but I guess I didn’t watch it long enough.