What sort of crazy ignition gimmick is this?

A friend of mine, later an electrical engineer, outsmarted himself with one of these. He knew the cap (condenser) in the distributor was no longer needed so he pulled it out. And of course at some point the CD unit died. He could not simply switch it over, without a cap. Some did not have a switch. They rather had terminal boards at the coil, and you could undo them and reconnect the original wires.

OP I WOULD NOT run that thing judging from outward appearance. And it is very likely some of the caps are bad/ leaky. Those essentially work like an electronic photoflash. The two big transistors are part of an inverter that takes 12V chops it up, raises it to a high voltage and rectifies it, then charges a capacitor up. When the thing fires (SCR) the cap discharged a big pulse through the coil.