Actually, (chagrined smile) I answered my own question.

the gameEngine . (dot operator) accessed a few functions already. One of those functions was the one that initialized the game. All I had to do was to make my drawGame function public, and voila! It was available under the dot operator, as follows:

gameEngine.drawGame()

It's important for newbies to understand the mechanics of how one section can call functions in another. Perhaps someone will write a tutorial on this. Thanks!