Hello Carlyhoover12,
Thanks for asking the Apple Support Communities for help with your account, a payment method, and for downloading a game. This verification can occur for a few reasons, but are mostly to ensure you are authorized to use the account, Apple ID, payment method, and the payment method is still active. Here is some info and articles to help:
1. This article talks about the payment methods you can use and states: Payment methods that you can use with your Apple ID - Apple Support
"To make purchases from the App Store, iTunes Store, or Apple Books, or buy iCloud storage, you need an Apple ID and a valid payment method."
"If you can't make purchases or update apps, including free apps, you need to update your payment method or add a new one. If you already verified that a payment method is available in your country or region and you're still having trouble, learn more."
2. You can change your payment method using the process in this help article: Change, add, or remove Apple ID payment methods - Apple Support
3. It's possible the system is trying to verify your account. This article talks about this: About payment card authorization holds from the App Store or iTunes Store - Apple Support
"When you update your billing information in the App Store or iTunes Store, or add a member to your Family Sharing group, a temporary authorization hold for a nominal amount might be placed on the payment method that you have on file. Like many other merchants, Apple uses authorization holds to confirm that your payment account is active and that you have funds available to make purchases."
4. Once verified, you can use the same article in step 2 to attempt to remove your payment method.
5. If you have trouble removing your payment method, please check this help article: If you can't remove your last payment method or use no payment method with your Apple ID - Apple Support
Thanks and have a wonderful day.