How to interpret Employment Elasticity in this text? In this VoxEU text, «Promising ideas for future research on the employment effects of minimum wages », how do I interpret the elasticity of employment?

I would think of it as percentual change in quantity of labour demanded over percentual change in minimum wage. However, if I google the concept, I get % change in employment associated with a % change in output. Ok, Factor Incomes = Expenditures = Output. However, although at a national level they are the same, at a micro level, I don't see how both definitions would equate...

Any help would be appreciated.
I'm citing the first two lines of the article you refer to (emphasis mine):


  The debate among researchers about the employment effects of minimum wages remains intense and unsettled. There is clear variation in the magnitude of estimated employment effects across studies, with the debate often being between an elasticity for low-skilled groups equal to (or indistinguishable from) zero, or an elasticity in the range of −0.1 to −0.2. 


Mechanically, you can always compute elasticities of any two variables w.r.t. each other at an initial point $b$, which is defined as

$$\eta_{a, b} = \frac{\partial a(b)}{\partial b}\frac{b}{ a(b)}$$

Simply googling employment elasticity gives you 

$$\eta_{employment, X}$$

where $X$ is the unknown. What is it, that employment is elastic towards?

The article makes clear that indeed, $a$ in this context is the employment rate, while $b$ is the level of the minimum wage.

Instead of googling, you could have looked at any of the studies cited in the article. The first sentence in Dube et al (2010) actually states that


  We use policy discontinuities at state borders to identify the
  effects of minimum wages on earnings and employment in restaurants
  and other low-wage sectors.


So they're interested in two related elasticities, one of which was the one you initially suspected. Their table 2 will give you some estimates of those elasticities.