Correct, they are not electrically fired; they are mechanically fired through a firing pin to a primer.
Pass enough electricity through a primer, it will go off. No mechanical firing pin needed. Have a link around here somewhere if you need one. Problems: (1) extra complexity, (2) you need quite a bit current at sufficient voltage, and (3) that means you have to lug around backup batteries equals more weight (in the military context ruck sacks are heavy enough without adding a car battery or the equivalent).
The smaller miniguns such as the XM214 that fire the 5.56mm NATO cartridge or the M134 that fire the 7.62 NATO cartridge use mechanical firing pins because that's what the ammunition needs.
The larger miniguns such as the 20mm M61 and 30mm GAU-8 on aircraft use electrically-fired primers, as does the M242 Bushmaster 25mm chain gun.
Alternative: a primer designed to be triggered by electricity. Problems: (1) again more complexity which means (2) costs more.
So while they do exist, they simply are not practical compared to good old mechanical firing mechanisms.
They are electrically fired. These weapons do not have firing pins. The have firing contacts. Energized through an electrical connection, the contact touches the primary as it cycles past and initiates it. Release the trigger and the contact is de-energized.