Yozora is mistaken friendship and love matters.
She definitely love Kodaka. But because she never has friend before, she thought that it is natural to feel like this to a friend.
That's why during 2nd episode of NEXT, she said "So friends can kiss too."
So King's game is one of her scheme to get her and Kodaka kissing.
I believe that Yozora is afraid to take a step to her relationship because she is afraid that her friendship with Kodaka will break.
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