Interesting. Well in that explanation it is very clear that the diode within the CDI is converting AC to DC but since a diode can only remove one half of the AC sine wave, it will provide pulsed (half wave) DC voltage.
The example Ropp provided is for an ignition system with an alternator but the KX diagram shows a magneto instead of an alternator. This begs the question of what is the difference between an alternator and a magneto and here is were it gets clear as mud. Various sources define them differently. Some say the only difference is that the magneto uses permanent magnets and the alternator does not. This explanation makes sense to me since the word magnet is in the word magneto. But other sources say the difference between a magneto and an alternator is whether the magnets rotate or are stationary. I tend to discount that explanation. Getting back to the point. Since both produce AC, I figure Ropp's example is helpful in understanding how CDI works on either system.
At any rate, we know the KX has a magneto and it has permanent magnets in the flywheel, so the magnets rotate.
To get back to the real problem, I would hope that when the new stator arrives it will have detailed instructions that will help with wiring.