I’d be VERY wary of drawing conclusions from differentials in Democratic turnout in these states. Consider Texas, for example: Democratic turnout could be down because Clinton and Sanders did not put a lot of resources into that state relative to the size of the state. As the article itself explains near the bottom:
Voter ID rules “could have a large underlying role” in suppressing turnout this year but it’s too early to know for sure, said UC San Diego professor Zoltan Hajnal, who worked on the study. “We can’t assess it yet,” he said.
I also think this focus on turnout puts emphasis on the wrong place. The question is why make it harder for folks to vote when there is no good evidence these laws are serving antifraud or public confidence purposes.