How is that better than just showing the flyer at the door to get the discount?
They can track response rates for particular flyers by pointing them at different URLs. Measurable A/B testing for physical advertising.
They can print A/B versions of flyers and collect them upon entry. No QR needed for this kind of measuring. :)
Eg, I was handed a flyer for a random nightclub with a QR code on it for cheap entry. You just scanned the QR code then showed your mobile at the door for a discount. This was 5 years ago too (Tokyo, Shinjuku/Shibuya).