I don't think it's an extension in the normal sense. When I installed it from the Ecosia site it simply added Ecosia to the list of search engine options. There's no mention of it in the addons section of Firefox.
[Later] What I said above applies to Pale Moon, which is a spin-off from Firefox 27.3.0. But when I installed it on Firefox 52.3.0 it did install it as an extension. So it appears that Ecosia has both legacy and current options covered.