I doubt it. For one thing they'd lose the ability to ensure you're who you say you are with TouchID, etc.

Presumably, if they wanted to do a web version, they could introduce Safari-only JavaScript APIs for verifying TouchID.

They could use Continuity-type stuff to have you verify the payment from your phone, that's happening in your desktop browser.

Which sort of makes sense with today's announcements, they said they had the ability to now detect between taps and presses with the Apple Watch, that technology seems like it could be easily integrated under a trackpad as-well...

Apple trackpads can already distinguish between a finger touching them and being physically depressed, though I don't know what it has to do with payments.

Thats a very different mechanism.

Of course, but it accomplishes something similar. Also, trackpads already have the two finger tap for additional actions (i.e. right click menu), and I still don't know what this has to do with the topic. :)

That's what I thought, but Apple Watch supports Apple Pay and that doesn't support Touch ID.

There are ways you could integrate this with a web site. You could use an authentication code sent on the backend to the phone for confirmation. It would basically be the same as any two-factor authentication. I'm just not sure which way it would have to go.

Or instead of NFC, maybe the phone is linked to Safari through a bluetooth connection and works with a specific Javascript API.

All of this, is of course implementation dependent. And at the moment, I won't think that we have enough information to rule it out.