I wish he had opened it up and shown the insides. I bet it's some fantastic assemblage of point-to-point circuitry.
They may have avoided having to use electrolytic capacitors. Or they might have used especially high-quality ones given that it was a specialized (and probably very expensive) piece of equipment.
I would have expected such a device from 1964 to have at least a few tubs in it, but the fact that it didn't require any 'warm up' time after he switched it on suggests that that's not the case.
Transistor devices had been around for years at that point; we were already making transistor computers.
Also, electrolytic caps are pretty easy to replace--they're big, clearly labelled, and it's not like the functionality has changed (a 100 uF capacitor is still a 100 uF capacitor).