Are you trying to add an actual credit card or debit card? Or are you trying to add a pass, ticket or gift voucher?
For credit and debit cards, make sure your iPhone's region is set to one where Apple Pay is supported in Settings->General->Country & Region. Link->Countries and regions that support Apple Pay - Apple Support
and follow the steps in the support document you posted from to add it. You don't need a button, email or app to add an actual debit or credit card to wallet.
If adding a pass, ticket, or gift card check with the issuer of the item for a way to add it to wallet as mentioned. You need an Add to Wallet button, and email or even a QR code provided by the issuer of the item to be able to add it to Wallet.
Link-> Add, use, and share boarding passes, tickets, and other passes in Apple Wallet - Apple Support
The button should look like this: