It is a Sierra thing, but not on every Mac.
If your Mac has a Touch Bar, use Wallet & Apple Pay preferences to add the credit, debit, prepaid, and store cards you want to use to make payments on websites that support Apple Pay. {emphasis added}
That answers your "special hardware" speculation. The Wallet and Apple Pay preference pane only appears when a Touch Bar is present.
I drilled down a little further in Apple Help and found…
Set up Apple Pay on your Mac
Choose Apple menu > System Preferences, then click Wallet & Apple Pay.
…<snip>...
Add a new card: Position your card in front of your computer’s camera so that it appears within the frame shown on the screen, then follow the onscreen instructions. Or click Enter Card Details Manually, then provide the requested information. Repeat for each card you want to use with Apple Pay. {emphasis added}
Which satisfied my curiosity. You hold the card up in front of the screen so it may be seen by the FaceTime camera.