As he explained in a speech published on Moon's Universal Peace Federation website (undated):

One of the great missions of Rev. Moon is to see how we can bring about a unification of the great religions of the world...and under the leadership of Rev. Moon - I had the privilege to present to the Security Council last year - a resolution for a dialogue among civilizations, among religions, among cultures, for an interfaith dialogue and I am happy to report to you that the following month, the United Nations General Assembly unanimously approved our resolution calling for an interfaith dialogue among the great religions of the world.

Of course, we can only guess whether there is any actual co-operation going on between Abdullah and Moon, but the UN conflab can clearly benefit both men: for Moon, there is a chance to promote an agenda that mirrors the Universal Peace Federation's "One Family Under God" concept, and for Abdullah the opportunity to drum up support for a "defamation of religions" (i.e. anti-blasphemy) resolution.

According to the UAE National:

King Abdullah's interfaith debate at UN headquarters will likely become the world's most well-attended cross-religious parley to date, with as many as 30 heads of state set to talk including George W Bush, the US president, the Saudi monarch and King Juan Carlos of Spain.

And it's already got off to a promising start, with a Saudi diplomat disavowing the "accusation" that Abdullah had invited Israel...