One advantage of a system like this can be the static nature of the objective function. If you set the rules up clearly beforehand (perhaps in a Constitutional amendment), then after a while the ebb and flow of two-party politics will balance out in the new reality (see Duverger's Law) and you no longer have to deal with gerrymandering.

I can't access the website either, but I'm really curious to see if their definition of fairness creates districts that violate the majority-minority rules in the Voting Rights Act