There are four things that immediately strike me about the Department of State choosing a Kindle over the iPad.
First, not everyone can afford to or wants to pay the premium price for an iPad. This goes for pretty much all Apple devices. Most of their computers are far more costly than other options, like the Kindle. So this will obviously save DoS some money. Just look at the picture; the iPad shown looks to have AT&T, so that means it costs a minimum of $550. The Kindle Touch costs between $99 and $149.
Second, Apple products are more popular with the creative types, not for cheaper, overseas learning programs. The security issue that they are probably most concerned about is theft, because they would sell for far more on the black market than a Kindle. The Kindles are a great product and do enough for the purpose they will serve.
Third, from what I have heard around the street, Amazon and their Cloud services already have a good relationship with several departments, such as DoS. It would make sense for DoS to manage devices centrally over the Cloud services they have already worked with at Amazon, and to use the devices already set up to run on them.
Lastly, $16.5 million and 2,500 devices is maybe a slight scratch to the business Apple does with their iPad devices. So this is in no way a huge loss for Apple or a huge win for Amazon. But it is a big win for the Department of State for not overspending on something more than what they really need.