Electrical current flows through your speaker wires. More current flows thorough wires with less resistance (i.e., wires with larger cross-sectional area....or smaller gauge). Therefore, the larger wires will carry a proportionally larger amount of current. However, in the absence of a cross-over, and ignoring any hysteria about skin-effect, I cannot think of any reason why the different wires in the cable you describe would be carrying different frequencies if they are all connected at the same place at both ends. The frequencies certainly would not be isolated to different wires as is somewhat implied by the marketing blurb.
As to your question about
"what PS Audio is trying to accomplish with this cable construction"
my thought would be that they decided to try something they could advertise as being somewhat revolutionary and cutting-edge in order to create interest and sell more cables.