They can't. Depending on how the chip is processed, the card number may or may not be transmitted at all, and if it is, it's encrypted so that RN can't see it. Rewards Network used to operate by being a man-in-the-middle where they check for registered card numbers when the charge is transmitted. With chip cards where the chip is processed (and not swiped), the actual card number is either not transmitted, or is encrypted, there's no way for them to tell.

Sending in receipts is a better than not having a program at all, because unless RN comes out with their own card processing system that they force the restaurants to use (which means chains will never join), there's no way around it.