Well, earlier in the scene, Belldandy and Jareth make a formal promise with each other that's nearly on the same level as a wish, so the system at this point is already primed.
As for triggering it...
“But neither of you were making a promise,” said Noike.
“True. But Jareth is more than simply a legitimate King. He has been recognized by both Heaven and Hell as the rightful ruler of the Goblins. There is also the fact that while he’s not a kami by any stretch, he is still an incredibly powerful Fey — probably the most powerful one on Earth. When you combine that kind of power with a formally recognized mandate to rule? And with two of us as witnesses to him presiding over such a vow? The Ultimate Force System would have acted on that, because in that situation that’s just as good as a First Class Goddess making a promise."
But if it helps, Marller, a First-Class Demon, was there as well.
As for triggering it...
“But neither of you were making a promise,” said Noike.
“True. But Jareth is more than simply a legitimate King. He has been recognized by both Heaven and Hell as the rightful ruler of the Goblins. There is also the fact that while he’s not a kami by any stretch, he is still an incredibly powerful Fey — probably the most powerful one on Earth. When you combine that kind of power with a formally recognized mandate to rule? And with two of us as witnesses to him presiding over such a vow? The Ultimate Force System would have acted on that, because in that situation that’s just as good as a First Class Goddess making a promise."
But if it helps, Marller, a First-Class Demon, was there as well.