It is mainly the current that burn the trace and or transistors etc inside. You don't need high voltage. I designed IC before, if you look under the microscope, it has metal traces, transistors, resistors etc. Just like real circuit! When even we need to modify the circuit and need to cut a trace, we use two needle probe sticking to both ends of the trace to be cut, then discharge a cap that was charged to some battery voltage. You can see the trace explode under the microscope.
Remember, inside the chip, heat dissipation is very poor, you pass a shot of current, it heat up and melted.
As for HV discharge, remember the even a very small capacitor charged up to high voltage have a lot of charge in the cap even though the capacitance is very low. If you short the cap, all the current discharged in matter of sub nano seconds, the instantaneous current is very high and melt any connections inside the IC.
HV discharge can easily reach hundreds of Amps of instantaneous current even though it last only less than one nano second. You burn relay contacts, and other large connections. I know, I work with 10KV+ circuits and we need to buy special relays with tungsten contacts, or else, it get burn just from a few arc and was like $50+ each. This is with just discharge from capacitance of a 2' coax cable that is only about 60pF.