If a parent or guardian purchases a Game will others in the family be able to play

"Purchase Sharing doesn't include subscriptions. But if you use Family Sharing, you can share your Apple Music family subscription, and your iCloud storage and Apple News+ subscriptions, with your family members."

from: What types of content can I share with my family using purchase sharing? - Apple Support - What types of content can I share with my family? - Apple Support

Buy additional app features with in-app purchases and subscriptions - Apple Support

It depends upon the game, who supplies it, and how it operates. If it is a simple third party app then yes, but if it involves subscriptions or in-app purchases then likely not unless they have a family level. Look at the app's information details on its download link and it should say what is allowed.