Very simply put, that's who we are. There are many similarities between IE cultures, and ADF was not founded as a purely Celtic organization. If ADF were a Neo-Pagan church, open to all versions of Paganism, we would have no real identity. Our focus on IE cultures helps us move from having an incomprehensibly huge focus to having a somewhat smaller focus.
For the best reason why, see this in the preamble the ADF Constitution:
Ár nDraíocht Féin . . . is the legal structure for a Neo-Pagan Druidic religion based on the beliefs and practices of the ancient Indo-Europeans, adapted to the needs and sensibilities of modern people.
This does mean that our rituals all fall into a general IE focus, too. An ADF Grove cannot do (for example) an Egyptian ritual or an Nepalese yakherding ritual for a High Day, or even as an official ADF rite. This also allows Groves to draw on other Pagan mini-communities for members, though, opening the organization up to Asatru, Hellenes, and many other types of Pagans. ADF has a unique identity that is partially caused by its diversity.
Who we are is also encapsulated by the somewhat amorphously-used term "Druid." We never really define "Druidic" or "Druidry" beyond a "polytheistic, non-dualist, non-sexist, non-racist, scientific, holistic, and ecologically oriented faith."² In general, our use of this term revolves around understanding the various Indo-European priestly classes as similar enough in function to mean that any IE priestly term would work, whether it was "druid," "brahmin," "flamen", or "Hierophantes." Due to the proclivities of our founder, we settled on "druid" as a term for what we're doing.
Of course, our name also translates as "Our Own Magic" (as well as "Our Own Drudiry"), so we aren't specifically tied to Druidry, even if our name is Gaelic.
¹ - This is a revised version of a FAQ I wrote for the 2005 GOH.
² - "The ADF Constution"