On the one hand It is a free system to spend your KPScore on.
On the other hand, I am certain it doesn't respond to the animation shown, it is entirely luck based, IMO it is better to just spend the KPScore on Bronze keys for BB7/CV7
Edit: To clarify, It is luck based as it is supposed to be, if the fortune wheel responded to the animation it could be easily exploited, BB7/CV7 keys have better prizes IMO and in the end the gift is a chance to win one of those big prizes and not the points themselves.