No so the window.Payment[1] isn't in the right place yet—according to Apple—to be ready for their use. You can read more in [2]. So eventually ApplePay.js would (I presume based on their language) disappear to some extent and all browsers could use the Payments API and Apple wouldn't need their own custom solution.
[1] https://www.w3.org/TR/payment-request/ [2] https://lists.w3.org/Archives/Public/public-payments-wg/2016...