Rails-api is a gem that configures rails in a more lean and mean fashion for API usage, it doesn't handle the json serialization. Mostly rails-api disables a lot of default rails features/middlewares that aren't needed when you're only building an API.
For json serialization you may want to look at Active Model Serializers[0], I found it much easier to work with than rabl, and it's also written by the rails-api group.
Hmm. Unless I'm crazy, RABL is a totally different thing for a different purpose. RABL is a tool (as is the analogous JBuilder, the default JSON-rendering-thingy for full-blown Rails) whereas Rails::API is a framework.