Ruri couldn't stand Akane because she was a stranger who - in her possessive child's eyes - was trying to enter her guild and her small group of friends to destroy it.
Once Akane's true feelings towards the game are understood, Ruri has no reason to hate her anymore. . . in fact, he sees her now as "part of the family".
That's why she doesn't disdain, but together with his brother she tries to make Akane and Yamada's love blossom. . . it's a way to keep them both close and at the same time prevent others from getting into the group and risking splitting it.