That's the root URL for the REST API when pretty permalinks are turned on. All WordPress installs have it,
When this answer was originally written WP 4.6 was out and only a handful of endpoints existed, and the plugin was needed for content endpoints, but they were merged in WP v4.7. The core infrastructure for the REST API has been available since 4.5, with functions such as
register_rest_route being available.
However when I hit the above directory even on sites that do not have the plugin installed I get data back.
This is endpoint discovery data! A list of all the endpoints you're allowed/able to access. You may notice a large number of endpoints if you have for example Jetpack for example. This is how apps can automatically figure out what your site can do, or check for the presence of endpoints.
Note that the information shared is only relevant to you the person accessing it. Endpoints that require capabilities you don't have are not listed unless you login as a user who can do those things. E.g. you won't see
POST endpoints for some content unless you're making authenticated requests as an author/editor or higher.