Here are a couple of very simplistic observations:
1) Not a big dog in the hunt regarding predictive power, but in the 2nd paragraph the writers state "In this article, we do three things. First, we recap our methodology. Second, we update the methodology for 2014, and we look forward to 2016." Sounds like they think it can be used to predict.
2) In the first chart one thing is clear -- the Republican strength has reduced during every Republican presidency analyzed. Reagan from -10 to -40 appears to be the least reduction. Likewise the Republican strength has increased during every Democratic president. Hmmm, now that I think about it, the fact that strength is cyclical and is at it's height for a party when a change in the white house occurs is not the most insightful analysis. Although it's always nice to demonstrate with statistics what appears to be intuitive.
3) When you consider the 5 components of the index, it's not surprising that the R's come out ahead, since they dominate at the state level and in the house. I think a more insightful analysis would suggest why this is the case. These guys seem to be pointing out the obvious to crow about the strength of the Republicans. I'm not surprised you find them "good political analysts".