I think a rivalry in this sense isnt about hating each other or anything. I think it`s more about trying to outperform each other. By having a sense of rivalry, it makes them try harder and better: singing, dancing, and being funny/interesting on tv shows, thus, their overall quality when performing songs will be better. However, this doesn`t make them hate each other or anything and that they are still friends. "Rivalry" can also mean, not only outdoing each other, but also helping each other too, like pointing out what they are doing wrong and what not. I think that is what Rika and the other older members are trying to say. Having a sense of rival feeling can help put a flame underneath Morning Musume, to "power them up" so to speak, cuz I think what Rika is saying is that the flame right now is kinda dull and low.