Today at Google I/O, a new Web Payments API was discussed at length which will help AndroidPay find its way to the mobile Web.
The API stores payment information you commonly use, and can identify new payment info as you enter it on Websites. It works independently of Android Pay, too.
In practice, it performs a lot like Android Pay for native applications. After the API learns your payment information, it offers it up as a default the next time you visit a Website. You can even check out with one touch if you’ve got a modern Android phone with a fingerprint sensor.
Google’s example was Shopify (which you can see above), which is an early partner for the Mobile Payments API.
Of course, an API requires developer support. It’ll take time to roll out widely, and may never reach the critical mass of Apple Pay unless Google gets bullish with companies to implement it.