In reply to NYCgirl, you're on a good track with your answer, but that's not entirely accurate. My PC's GPU and CPU consume quite a bit of power at load, because I play real, demanding games, not just casual Facebook games. The power draw is very different from those types of games.
Of course, playing games offline will not have an appreciable dent in your electricity. The only way that would make a difference would be if you were to shut off your Internet equipment while playing games offline: the modem, the wireless router, and any other things using the internet connection.