As Apple's written in its Support Website:
With the release of macOS Sierra and iOS 10, Apple Pay is coming to Safari on your Mac, iPhone, and iPad. So the purchases you make on many of your favorite websites will be faster and more secure than ever.
Now, this opens a whole new world for online purchases, especially because all you'll have to do to make purchases online will be to lay your finger on the Touch ID sensor of your iDevice and that's it.
What I want to say is this new Apple Pay's feature implementation and utilization is all up to developers, and as such, we can just try to imagine what to expect this fall.
As you mentioned in your question above, developers who may think of having a 'continuity' feature for their Apps, may think about having Apple Pay enabled on their Apps website in order to provide their customers with even further functionalities which however will have to be purchased first.
Even if there are many ways this new feature could be used for, we're very sure it will affect many of the major (and not only) online markets, probably like Amazon, eBay, etc..
Talking about Beta OS from Apple, as this feature is from the upcoming new release of their OS for Macs (macOS Sierra), you may find useful to know all the Beta program will accept Public users starting from July, in case you'll want to enroll and try it before the Official release coming this fall.
For further details about the new macOS Sierra, I'll link you Apple's webpage for it.