I don't know how to add a PlayGame () object.

I’m following this.
and I’m trying to follow it exactly.

I’m at about 4:21. There’s got to be something simple I’m overlooking… Does anyone know how I add the PlayGame() object?

In order for methods (or functions) to be attached to the event system they must be public, have a return type of void and have 0 to 1 parameter.

So, your method declaration should look something like:

public void PlayGame()
{       
}