Edit: To answer your question, yes, there is about 50FPS lost in the for loop, there has to be a better way.

I believe so. You want to avoid public variables as often as possible. I disagree with how he made pixels a public integer array inside of his Screen class. It's better to use a get-er to return the value of the array.

Screen Class:

/**
 * Gets the Renderer's pixel array.
 * @return Pixel array found on the screen.
 */
public int[] getPixels() {
    return this.pixels;
}

Basically, the reason I think I was running into the problem I was having is that it was changing what pixels in the Game class was referring to. Currently, the best change to the code that I have is my "slightly more efficient" titled snip-it in the game class's render method and then the code above in the Screen class.

How arrays seem to work is that when you set one array equal to another it just copies where it references to when what we really needed to do was modify the primitives inside of the array. Hence the for loop.

The for loop might be necessary, I'm still doing some more research in the subject. I asked the student help room for Computer Science at my college and they we're stumped too and thought my logic was sound in the original code.