Purpose of correlating docking score with catalytic efficiency(Kcat/km) What is the purpose of correlating docking score with catalytic efficiency (kcat/km)? 
I saw some papers are doing this, is it to validate the docking protocol? 
Lets say the docking protocol is correct, the docking score will positively correlate with kcat/km?
What is the purpose of correlating docking score with catalytic efficiency (kcat/km)?


This is specific to the enzymology of paper you are citing. If the solubility of your substrate is lower than your Michaelis constant (K_M) you cannot fit to a Michaelis-Menten curve and can only get the slope of the initial straight part of the curve, which is the catalytic efficiency (k_cat/K_M). Ideally K_M would be better. But in generally catalytic efficiency ought to correlate with well calculated ddGs of ligand binding.


  I saw some papers are doing this, is it to validate the docking protocol?


Totally. Docking finds were ligands bind. Although the energetics don't match too well the experimental kinetics as of 2019.
The catalytic efficiency (k_cat/K_M) is the ratio of the turnover (k_cat) over Michaelis constant (K_M). The Michealis constant is in turn the ratio of on-rate over off-rate plus turnover. The &Delta;&Delta;Gibbs of the ligand ought to correlate with the ratio of the on-rate/off-rate, while the turnover is unrelated.
The turnover should correlate with the difference in energy between the substrate bound form and the transition state. This is the realm of theozyme design and requires correctly protonated ligands and protein, but when it is you get a nice transition state hill (e.g. personal example).

There are a few "ought to" in the above. Docking and force-field energy scores are not precise. The paper you refer to is doing very advance docking (akin to dynamic undocking) and, not accidentally, the ligands are very flexible and rather soluble.


  Lets say the docking protocol is correct, the docking score will positively correlate with kcat/km?


A positive correlation coefficient just means that generally both the catalytic efficiency and docking scores increases or decrease together. If a metric "worked backwards", such as &Delta;&Delta;Gibbs (more negative is better), you would want a negative correlation. What you want is a strong correlation, with the sign a result of the nature of your metrics.