I got an email about a purchase of a game that I didn’t make

more than likely they sent you spam in the hopes of you being frightened into giving them your login and password. Do not respond to that email or click on any links. You can report fraud to Apple. see below

Avoid phishing emails, fake ‘virus‘ alerts, phony support calls, and other scams

https://support.apple.com/en-us/ht204759 

If you see an unfamiliar charge see this link:

https://support.apple.com/en-us/HT201382

View, change, or cancel your subscriptions

https://support.apple.com/en-us/HT202039

to see your purchase history from Apple see this link:

https://support.apple.com/en-us/HT204088