Come on, the math is not hard here. The question allowed multiple responses and in one case the division was done using the number of responders instead of using the number of responses.

And you got your conspiracy exactly backward. The result was to artificially inflate the percentage reported for emacs.

 $ say '85+65+78+519+355'
1102
 $ say '85/11.02,65/11.02,78/11.02,519/11.02,355/11.02'
7.71324863883848
5.8983666061706
7.07803992740472
47.0961887477314
32.2141560798548
 $ say 138/11.02
12.5226860254083
[download]

So just drop emacs' popularity from the reported 16.25% to the correct 12.5%.

All that is left is to figure out if the mistake was motivated by the preparer being an emacs fan or because they felt sorry for emacs fans and whether it was intentional or accidental. q-:

Update: Oh, and the percentages reported for Notepad++, Eclipse, and VisualStudio might well also be inflated by x1.3 (hard to say for sure since the counts were not reported for them).

Update: Though, I kind of find the 30% higher percentages more accurate. The problem was probably that they put the counts into the graph software and it is what provided the percentages. Makes me wish for a "Venn diagram" chart where the area of each shape is proportional to the number of people who chose that option and the areas of the overlaps between shapes is also proportional (to the number of people who chose all of the corresponding options).