No, most retailers can't accept online payments (or "like an online payment") - if they want to, that's a different kind of agreement with different (higher) fees and more liability for fraudulent transactions.
If they want to book it as 'card present' transaction, then they have to follow the 'card present' guidelines - which, by coincidence, would require them to see the actual card, not just it's magstripe data in some fancy device.
If they want to book it as 'card present' transaction, then they have to follow the 'card present' guidelines - which, by coincidence, would require them to see the actual card, not just it's magstripe data in some fancy device.