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Stata is fairly ubiquitous in statistical circles, especially those working in econometrics. While I preferred using Stata in academia, it is expensive and R is similar, just not as easy to use.

Agreed. Stata makes common statistical operations easy, and the higher-level licenses are extremely powerful. But I prefer R because it's so much more flexible when trying to perform more complex data manipulations. Plus lots of statistical papers with new techniques include R code.

As noted in other replies, this isn’t the Stata homepage, but rather an academic page about the use of the program. Apologies for the confusion, I chose it because it has images that neatly match what Silver shows.

That isn't the home page for Stata, that is a page put up by Reed about where to find Stata on their computers. Go to stata.com

Sata is proprietary.