Free Piston Stirling Engine Tuning Capacitor - Series Vs Parallel
I can't seem to read the paper via your link, so this is a generic answer:

Series-tuned circuits have their minimum impedance at resonance, while parallel-tuned circuits have their maximum impedance at resonance.

It would seem that the idea here is to nullify the effects of the leakage inductance of the generator coil on power delivery, so minimum impedance is what you want.