Can I still approve each game before my kid downloads?
Is the approval process for an Apple Arcade game like it is for other App Store downloads?
Not sure. From Join Apple Arcade - Apple Support:
With Family Sharing, when one person in your family subscribes to Apple Arcade, everyone in your Family gets access.
Since there are no costs involved you might not get an approval request for Apple Arcade apps. Then again according to Request and make purchases with Ask to Buy - Apple Support Ask to Buy can apply to free content too, so perhaps Apple Arcade is treated in the same way.
Unless someone has a definitive answer you might have to volunteer to find out. My kids are all grown up.
tt2