Just wanted to add some thoughts on how one could try to make this RESTful. First, if it were me, I'd pick a media type that can express hyperlinks in JSON (since JSON knows nothing about hyperlinks), maybe something like HAL [1]. Next, I would define my link relations for this API, which in this case would be a collection of countries and the countries themselves (so at least two different types of resources).
After creating the representations of each of these resources, I would then create URI templates in my root response (I guess found at /rest) that allow for the searching aspect that this site is providing, which would be something like:
{
"_links": {
"search_by_name": {
"href": "/rest/name/{name}",
"templated": true
}
}
}
I may build on to this to provide other resources, like a collection of capitals, each with a link to "/rest/capital/{capital_city}", or a resource of currencies, linking to "/rest/currency/{currency}".
The goal of all of this would be to tell the client how to find resources rather than having that hard-coded into the client. These are just some first steps toward being RESTful, and there are lots of different directions you could take this and still be RESTful.
edit: example was incomplete
[1] http://stateless.co/hal_specification.html