I acknowledged in my comment that there were a limited number of data points and that other variables would have to be introduced to arrive at a satisfactory explanation. That said, correlation is, by definition, always a matter of the degree of correlation and correlation itself is seldom the same as causation, even if the correlation is 1. (The example of Brady v Mallett is, as you intended it, uninteresting statistically, so I won't even address it.)
However, the correlation between play selection and outcomes is not completely random in this case. In fact, with the qualifications that I mentioned in my original post and which I repeated above, if you make Winning and Losing the dependent variable and you make Run/Pass Play Selection the independent variable, the R-square of a regression of those data is north of 0.9, suggesting that the correlation is not "loose," but, at the very least, "observable."
As someone who spends a lot of time with statistics, I hasten to add again, as I have already stated twice, that the limited number of data points make it impossible to draw any final conclusions from the analysis, but one conclusion you cannot draw is that the analysis suggests nothing.
What the analysis suggests is that the exercise is incomplete and that, in the end, the dominant explanatory variable could be completely different than play seleciton, but that play selection will be meaningful.