I skimmed it. All it shows is that Lott's results are not robust to changes in specificataion and addition of new data (lot's dataset ended in 1992, this one in 1999). The only valid conclusion one can draw from Donohue's results is that concealed-carry laws don't affect crime rates very much one either way. The author is a lot more circumspect in his statements in the research paper than in the article.
It may be that the rates of violent crime, after dropping at the initial passing of CCW, stabilized for several years at the new, lower level. This would tend to appear to dilute the crime-lowering effect of CCW, if such exists.