Actually I think the joke was that Japan always completed the ritual, because in Japanese horror often the humans pretty much die and the evil can't ever be completely vanquished.
I did laugh when the schoolchildren won, especially given the American guy shouting "Fuck you!" at them on the telly while they celebrated.
It just seemed odd that the elder gods didn't really care which ritual was completed as long as one of them was, and that in itself seems to suggest the actual nature of the ritual was unimportant? And this is born out again by the fact that they're just ordering the guards to shoot the two of them, the only caveat being that he had to die first.
Your comment about the film poking fun at the horror genre without wanting to be part of it rings true for me. Scream was funny, and Scream played around with horror tropes/homaged the genre, but it was also, at heart, part of the genre. Yes it got funnier as it went along, and less scary as the villains were shown to be quite inept but in places, and in particular in the opening with Drew Barrymore, it was damn scary.