How high is *your* high voltage?
Any idea what it drops to when a discharge is occurring?
What is the highest number of hits per second expected?
Assuming the high voltage is positive with respect to GND, then a very high impedance voltage divider driving a high speed Schmitt-trigger-input CMOS gate, such as something in the AC series, will give you a signal any counter will be happy with. For example, if the HV is 8 kV and the series current limiting resistor is 20 M (as in the video), then a 10K resistor between the cathode (aluminum disc) and GND will divide the HV down to 4 V, pulling the input of a 74AC14 hex inverter high when there is a discharge. In between sparks there is no current, and the 10 K resistor holds the inverter input low. The CMOS gate can handle over 1 million transitions per second, so the more difficult part is to find a low cost counter that can keep up.
Chip, decoupling capacitors, input protection diodes, $1.00.
This circuit will not capture two overlapping arcs. If an arc in one area starts before an arc in another ares is extinguished, the circuit will see one long arc instead of two short ones. The circuit requires a small time gap between arcs. It can be less than 100 nanoseconds, but it has to be there.
Where are you located?
ak