The post asks the question "could ‘Facebook Deals’ be the app that kills Groupon?" I believe they are both going after separate things. Facebook wants users to check-in and explore their world through the Facebook portal and by doing this you get rewarded with little perks (deals). However, Groupon wants users to explore their world cheaper. They offer deals to services and products not known about before.
Groupon = Explore A new World.
Facebook = Take advantage of a world already explored.