Colour me sceptical; the benefit of round pie charts is that all points are equidistant from the center, so there’s nothing particularly implied by placement of each pie slice.

Free Exchange links to art blogger Kriston Capps (Grammar Police) who links to Six Apart’s Anil Dash and sociologist Kieran Healy (Crooked Timber). It’s a hot topic apparently.

Healy points out that the square pie chart is not a “mosaic chart” which it superficially resembles. To explain mosaic charts, Healy links here (pdf).

Finally, several of Healy’s commenters assert that the chart is a sight gag. The white square is the door into the afterlife with the data arranged accordingly. It’s supposed to be distracting (as your life passes before your eyes…).

But it’s a terrible design. The response values are in four different places. (And as you note, one section isn’t even labeled.)

More importantly, we have a harder time interpreting area than we do length. (Same problem that pie charts have.) I look at the “U” shaped figure representing 24%. It looks like it’s three times bigger than the 10% respone along the top line of the chart.

In fact, this graphic would have expressed more simply and usefully as a 2×5 table.