Hello S.K.R
Welcome to Apple Support Communities. We understand that you would like to either block an app from one of your son’s devices or restrict his time on one of his devices. We are happy to help.
You are able to use parental controls on his device using the steps here: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support This will allow you to restrict Game Center, prevent web content, etc.
You also have the option to use Screen Time on their device, which limit the time they can use their device. here’s more information on Screen Time: Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support
Let us know if you have further questions.
Take care.