"Look," whispered Chuck, and George lifted his eyes to
heaven. (There is always a last time for everything.)
Overhead, without any fuss, the stars were going out.
The two guys mentioned above set up a computer for Tibetan monks, which is able to pronounce the Tibetan sounds in the permutations that make up the nine billion names of God. Since this is supposed to be man's ultimate destiny, the world would end at that point. The last few passages of the story are above.
One of the major themes of the story is the idea of a divine plan. The world really is ending after the utterances of the nine billionth name. It also implies that the pursuit of technology is self-defeatist, and that mankind has no choice but to fulfill the divine plan.
So you see, it does say a bit more than something about the existence of God.