Turn Off Apple Arcade Family Sharing

From Apple ID & Privacy - Apple Support:

If Family Sharing is enabled for Apple Music, Apple TV, Arcade, or News+, family members will continue to sign in to each service using their own Apple IDs, keeping their individual libraries and recommendations private, while taking advantage of the family plan. 

As far as I am aware if you are part of a family sharing group and one member subscribes to Apple Arcade then all other members of the family get access to it for no additional fee. As you have found there doesn't be an option not to share.

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Did you see this already - you can choose to hide individual items or choose not to share your purchases in your Family Sharing settings