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putting a capacitor across a spark gap will cause the secondary side of the coil to spend more time generating a higher voltage before the air(or air/fuel mix, in the case of an engine) breaks down and conducts the spark... with some very low ESR, very high voltage capacitors, I can see how that would cause a shorter duration, higher intensity spark: capacitors charge until the arc occurs(which lengthens secondary voltage rise time), then they dump their charge through the arc.... but that's exactly what CDI ignitions and low resistance plugs/wires do already. for a given amount of energy fed into the coil, they trade off spark duration for spark intensity. this isn't always a desirable compromise depending on the situation, especially when you look at plug/wire/coil life during this kind of operation(not to mention the havoc you can wreak on any circuits that are sensitive to induced current via EMI). it does seem like a way of getting CDI characteristics out of an inductive ignition setup though.
I'm not entirely certain what is going on with the second video, not enough time to analyze it at the moment.
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