While I think it's a clever spin. I don't see why Groupon can't do the same in an instant if it proves to be effective. If that happens these guys just become another Groupon clone competing on lower rates for merchants.
I even see a deal on Groupon Now which is $5 for a $9 sandwich. http://www.groupon.com/now/deals/5-for-9-at-nyc-bagel-deli-2...
That said, I fully agree it doesn't necessarily mean anything that Groupon can do it, too. There's plenty of room for competition.
To users, $20 worth of food doesn't tell them anything about what they're actually going to buy when they arrive at the venue, whereas $1 for a $2 cup of coffee specifies exactly what they'll get. You might also only spend $18.50 of your $20 credit and can't find something worth ~$1.50 to buy, which can leave a bad aftertaste for some people.
Also, this allows merchants to prepare much more effectively by overstocking on the items being featured. Or they could discount an already overstocked item just to get rid of it.
All in all, people visit restaurants for specific (signature) dishes, not for the restaurants themselves, so it all fits together.