The light part means: it doesn't drag a huge framework and code and complexity you don't need with it. It uses less resources than it would if it was doing that.
I would actually say that Travis CI is a Rails app, Rails is just not taking care of HTTP, but we use large parts of the Rails stack in many of our applications (Travis CI is a fully distributed app).
Our API app used to be a Rails application, but we ended up writing our own object serializers etc, so that the controllers were actually more or less just calling out to one method.
When we reworked our API, authentication, etc, we switched over to Sinatra.
The light part means: it doesn't drag a huge framework and code and complexity you don't need with it. It uses less resources than it would if it was doing that.