@Grant, fascinating paper! I had read about the two brothers in the popular press, but this is the first time I've read anything about the MINE/MIC algorithm. They provide an intuitive explanation at the beginning of the article (third link in your list).
The benefit of the technique is looking for fit, regardless of the relationship between variables. To be of big benefit we would need data where we could imagine finding non-linear relationships - otherwise I would imagine it is computationally cheaper to just test a linear regression (though I don't know if that is true).
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