It's a pity they use pie charts to show off their software. At least the don't show them in 3D. (And just to make it clear: there is no use case where pie charts are the best solution. At best they are an acceptable solution.)
Even worse is the "Sales Ranking" in the first example, clearly the size or area of the entries is not proportional to the differences in sales, instead it is highly misleading to display the data as a perfect triangle. The TreeMap-esque "Qty by Product" is also useless -- is Cup larger or smaller than Glass? Stacked bars for "Location by Year" is another obfuscated mechanism for delivering "information" -- which was the best year for Warehouse?
Use bars showing percentage. This way you can compare the values to a scale on the side and to each other. You can't see a difference easily on a pie chart without annotation. With enough values, you likely can't tell 5% from 10%, and difference between a fragment on the left from a fragment on the right.
This is even worse in 3d pie chart which doesn't even preserve proportions in areas/angles, so splitting in 4 parts, bottom/top will be larger than left/right.
Pie charts are not about the raw numbers, they are about quickly and roughly showing who ate how much of the pizza. In many pie charts, 5% and 10% looking similar is a benefit, not a problem (because in many cases 5/10% are effectively the same - minor but non-negligible portions). Bar charts are not a great option for this.
I think it's better to say that "for most people there is a better alternative" than to say that pie charts should never be used.
EDIT: If you are showing who ate which parts of a pizza (to be pedantic) I'm sure a pie chart may be the best case solution. My favourite use of pie charts is to compare the harmonic series and the series 1/x^2, but then again this latter example is not really a traditional pie chart.
