Earlier quoted context omitted.
The plot is showing that there is a negative selection bias in the reporting of stories about minimum wage. That is, that stories suggesting that increasing minimum wage has negative effects (increases unemployment, etc) are overreported relative to stories showing a positive effect from an increase in minimum wage. I am only repeating what the paper says; I don't claim to have validated their methodology or sources.
That is an incomplete summary. Their conclusion is that despite this larger than normal selection bias, the minimum wage appears to have no impact on unemployment. The paper's abstract, discussion, and summary all mention this as part of the central thesis - why leave it out?
So the conclusions the paper draws w.r.t. elasticity aren't that interesting; we'd need to know why the bias exists before it is particularly useful. I'm a bit suspicious of using 'meta-analysis' at all because that just means that the faction that repeats themselves the most with low-quality research gets to pick what the elasticity is.
In theory we shouldn't need 200 studies to make a claim, we should need 1 or maybe a small suite (like, 5) of very high quality studies that intellectually honest economists struggle to rebut.