@Glomoro—
You may well be correct, but there's a particular problem with the episode if you are.
In eating challenges of that sort, vomiting is a disqualification even if truly only one person is eating. If the disqualification were in vomiting, then there's no indication that the attempted fraud were detected. The situation is really no more or less funny that if just one girl attempted to eat the thing but vomited.
I quite agree that “Urgh!” is not a sound that one normally associates with burping. But we're looking at a translation; I don't know what sound were made in the original. And, if someone in a group vomited, it would be surprising for another person to form a question or expression of surprise from the sound of the vomiting.
Still, the whole episode is so awkward that I don't say that you're wrong.
ATTN:
@Hachi015