What's Jewish about the American Jewish World Service?

The press is abuzz with the funny video about the American Jewish World Service, which last year doled out $22 million to over 400 organizations around the world. They really used the star power effectively to promote the organization. Yet, the video - and the AJWS, raise some questions in my mind.
Sarah Silverman has the money line when she says, "The probably don't help any Jews. I mean, like Jews are fine, you know?"
Asking about the name Julia Louise Dreyfus asks, "Is it a world thing? Is it a Jewish thing?"
The dog (which I've never heard of, apparently called Triumph the Insult Comic Dog) says that instead of AJWS, the organization should be called, "Something simple, like "Jews Helping Goyim."
What is the AJWS? After all, I've never heard of it before? The AJWS website says that,

American Jewish World Service (AJWS) is an international development organization motivated by Judaism’s imperative to pursue justice. AJWS is dedicated to alleviating poverty, hunger and disease among the people of the developing world regardless of race, religion or nationality.

Sure, Judaism does instruct us to pursue justice. But does that make the institution Jewish? While I have no doubt that the AJWS does great work, it seems cheap, even inappropriate to call it "Jewish." Other than the weekly Torah portion, I fail to see anything Jewish about the organization. I'm sure you don't have to be Jewish to give money or sit on the board (although most board members seem to be Jews.) You don't need to be Jewish to receive money either. Is justice just a Jewish ideal? Isn't it also a Christian and Muslim principle? Why not then call the organization the AJCMWS?
This raises, in my mind, the question of how we even identify Jewish organizations anymore. They used to be connected to Jewish causes or Israel or Jewish education, but seemingly no longer. In some ways, the AJWS allows Jews to think that they're practicing Judaism, without doing anything particularly "Jewish" at all.