I don't think the argument presented there works.
Consider the example with A, B, and C at the end. It claims that approval voting would probably elect C, but why? If the voters apply perfect strategy, B supporters won't approve C, and B will win. The same is true of range voting, where B supporters will give C a rating of zero.
It does not seem escapable that a majority voter block can dictate their wishes on the whole population by exaggerating their stated preferences.