Indeed, you don’t need to specifically enroll into Apple dev thing. What you need is to approve your domain with Apple. APM addon does it for you. Just go to Stripe Payments -> Settings, “Additional Payment Methods” tab and click “Autoapprove Domain” button.
This is all you need in order to be able to access payments via Apple Pay. You can test if it’s working by trying to make a test mode payment on your site.