How Good are Center Games?

I played a Center Game, and successfully played a checkmate in 13 moves. Would the Center Game be useful in any other game I play, and will this be considered a Scholar's Mate, since the checkmate was carried out by a queen and bishop? Could this perhaps be called Scholar's Mate, Center Variation?

Nice game and good job at seeing your opportunity. If by good you mean is the Center Game a good opening,yes it is; especially newer players; it is the fundamental opening. It is a straight foreword, easy to understand opening,that is very good for teaching chess opening principles. It's a good place to start learning a chess opening,from here you can quickly move into a number of gambit openings,such as the Danish,Scotch,and Goring, This really isn't a Scholar's mate,since it didn't occur in the first four moves of the game,rather,it's a king side attack where you induced black to make some mistakes,then flushed out his king and mated him;all things considered,a nicely played game for you.

Good summary from badger-song. I should add that once you advance and start to play very much stronger players, the Center Game won't pose those stronger players very many challenges that they can't easily handle, and you might at that point want to start looking at the Ruy Lopez which will set them longer range strategic problems, but for now the Center Game is a pretty good choice, I would say. As badger-song writes, a nicely played game.