They didn't explain anything. You're referencing one quote from a UWM professor. They said that slow growth has to do with the industries in the state AND also mentioned that the reason Wisconsin is grouped in with the states that also have their data represented in the article is because the states share common industries and structure.
The article also linked to
this study showing the "non-political roots" of Wisconsin's problems. As the article notes, Wisconsin has experienced slow growth rates due to its reliance on aging industries like manufacturing plants, paper mills, and metal foundries.
If you had bothered to read the article, you would know that WI's slow growth rates are nothing new:
Well, that's just politics. Republicans blame bad job numbers on Democratic administrations. Democrats blame bad job numbers on Republican administrations. Neither side really cares about consistency or accuracy.
It's worth noting that, contrary to your claim, Wisconsin under Walker has faired better than Illinois under Quinn in terms of job growth. The chart cited by the article you link shows job growth from December 2010 to December 2013, but there is more recent data for us to look at. Since Walker took office in January 2011, Wisconsin's unemployment rate has declined by 1.9%, from 7.7% to 5.8%. Since Quinn took office in February 2009, Illinois' unemployment rate has declined by only 0.6%, from 8.5% to 7.9%. There are more factors at play here, obviously, but it is simply erroneous to claim that Quinn has a better jobs record than Walker.