I usually hate it when newspapers waste most of their space poorly defining terms, leaving no room for the actual interesting bits. (This is especially true in science articles.) This article, however, would do very well to mention what Foursquare is. I assume it's not the elementary school ball game, since that doesn't involve any sort of checkins. Nonetheless, how cool would that be? I would totally go to McDonald's if I could play four square while waiting for my food.
Take away from the article: McDonald's is a tough subject for piloting a FourSquare use-case. Too ubiquitous of a brand to be "discovered", customers probably not interested in location games, and how much more can you sweeten a deal at McDonald's.