In my impression that malicious tendencies of Yayako (the name itself!) are described very explicitly in the way she tries (successfully) to make others avoid Hanabi, something which she continues doing in the new school which is a trait of a pretty bad character in any culture I guess.
I talked to my daughter, who just finished 6th grade elementary school, about that scene and for her it is clearly bullying. The Undokai in general is a way to perform as a group no matter what, it is actually a lesson in group behavior rather than competitiveness because anyway the efforts (or failures) of one single person could rarely affect the overall outcome with soo many people in one group.
Personally I think the main “teaching” of the Undokai is to be able to accept the fact that there are people who are capable of doing certain things and other who are not but still everyone gives their best (and should not be judged on the result). From a westerners point of view I quite hate it, like really. It is long and dramatic and somehow unnecessary Like I really don’t see the point of training so hard with a group so large and inhomogeneous that only chance can decide who wins but you have heartbroken kids at home crying for at least one whole day in case they are in the losing team…
The overall situation appears to me as if Hanabi failed in building up a large enough clique to protect her from group dynamics due to her character which seems to be a bit of a dreamer. It looks to me as if Yayako actually sees her as a potential thread, she might be pretty enough to endanger her position as the “popular girl”. There are Mangas I read with issues like that in that particular age group where pretty girls had to make themselves unattractive in order to be able to keep friendships with their not so attractive friends which is something that current Hanabi probably wouldn’t be able to think of as she seems a bit socially oblivious.