App Store has charged money for the game I don’t have

Where are you seeing this charge exactly?

Did you ever have that game?

If so, did the game have a free trial?

If so, did you ever cancel it?

Try the steps here: View, change, or cancel your subscriptions - Apple Support

Deleting the App, does not cancel any associated free trials or subscriptions. Follow the steps in the link above to cancel them.

Then contact iTunes Billing for a refund: iTunes Store - Contact Us - Official Apple Support

Normally, all sales are considered final, but you can ask for a refund.

If you have received a confirmation email, click the Report a problem link at the bottom.

Purchases problem

If necessary, contact iTunes Support. Either use the form or scroll to the bottom of the page in the 2nd link. Follow through the screens to get a chat or telephone option.  You may need to pick a problem that is slightly different than yours to get a chat option.  

iTunes Support

iTunes Support – world wide

You need to cancel the subscription yourself, we cannot do it for you. You need to do it yourself. Follow the steps in the link above.

Then contact iTunes Billing for a refund.