You can't just generate energy from nothing. A flywheel stores energy, it doesn't create it. So yes, they got something wrong.
It's clearly not just a normal flywheel, perhaps it can convert some other energy form into electricity? (We call them "generators" don't we?)
When I think of the "motor-generator" component of a flywheel-based energy storage device, coils and magnetic poles and all that electromagnetic to/from mechanical energy conversion stuff comes to my mind.
Electrostatic to/from mechanical energy conversion is known [1] [2], but not to my knowledge known for sustained high power and energy density appropriate for practical flywheel-based energy storage.
Intriguing to consider that Dr. Post's research might be going in such a non-traditional direction as electrostatic motor-generators. Perhaps there are some incremental efficiency gains or design simplifications to be had in using the flat plates, good insulation and high voltages characteristic of electrostatics instead of the big coils, cores and high currents of electromagnetics.
That said, there's no free lunch: No matter which electrical-to-mechanical-to-electrical energy conversion mode used may be, the energy stored remains rotational kinetic energy, thus limited by the same critical physical limitations (failure modes, maximal energy density, maximal power density) of traditional (electromagnetic, to date) flywheels.
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Using electrostatics to pump up the flywheel is certainly interesting (I wish the article had even the slightest detail on it), but it still doesn't create energy. (Or collect energy from some untapped resource.)