Why do I have to update payment info to download free game?

If you can't choose None when you edit your Apple ID payment information

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing

Any app, such as most free games offer in-app purchases. You cannot download any free app which offers in-app purchases unless you have a valid payment method tied to your account.