The relation about FOM and power extraction improvement
I'm not familiar with the nomenclature in this area, but I've got an idea where things are coming from. The journey begins with a question of "How much (electrical) power should I expect from my piezo generator?

A piezo generator is roughly a capacitor. If I excite the piezo generator at a given frequency, I will see an AC voltage \$V_{PZ_{OC}}\$. I might imagine that my system could be modeled as a current source in parallel with a capacitor, making imaginary power. My circuit might look something like the following:







simulate this circuit &ndash; Schematic created using CircuitLab

In this case, I would say the complex power could be characterized as:
$$|P|= \dfrac{V^2}{Z}=V_{PZ_{OC}}^2(\dfrac{1}{2\pi fC})^{-1}=2\pi fCV_{PZ_{OC}}^2$$ 

This is the magnitude of the energy required to create an open-circuit voltage across an ideal capacitor. If this was a perfectly adequate description of a piezo generator, then you probably could never recover more energy than this value. If nothing else, this does provide a useful baseline expectation of system performance that should help reduce the impact of physical size differences.

Your figure of merit (FOM) is basically a ratio of recovered power to this "ideal baseline" case. The multiplication by 100 reflects the conversion from a ratio to a percent. 
$$ FOM=\dfrac{P_{measured}}{P_{baseline}}=\dfrac{P_{measured}}{2\pi fCV_{PZ_{OC}}^2}$$

In your paper, they advertised a FOM of 4.93 at resonance, meaning their measured power output was 4.93 times higher than the baseline value. Saying it another way, their FOM was 493%

I'm not sure where the \$2\pi\$ got off to in the FOM