Now, you knew I wasn't going to let Mock's comment go by without finding out for sure. Apparently game is the most common terminology for a complete curling competition. Match does pop up from time to time, though. A tournament is called a bonspiel.
To learn more:
Somewhat surprisingly, curling is not especially popular in Vermont. It is, however, quite a big deal in nearby Quebec, as Mock's comment would suggest. Yet another argument for DirecTV to carry the Canadian stations!