Reporting back on my experiment:
I was able to get driver.manage().window().getSize() to return something. However, I don't know what object it retuns. But I could see that I am getting the screen's dimensions by converting it to string and printing it out.
The output looks like a Python tuple, e.g., (768, 1184).
Anyway, my background is QA and my level of any programming language is limited to writing scripts and googling syntax. Java is not an exception. So, I did a what works for me, though it is probably not the most efficient or elegant codewise. I converted the returned object to String, split it into string array, get the width and height strings and convert them back into integers. You are probably laughing your behinds off right now, and if you are, please suggest a better way after you are done laughing :-).
String[] dimensions = driver.manage().window().getSize().toString().split("
\\D");
int screenWidth = Integer.parseInt(dimensions[1]);
int screenHeight = Integer.parseInt(dimensions[3]);
And now, I have my screen's dimensions for use in my script.
I might have been able to use the dimensions.getWidth() and dimensions.getHeight() methods and not have to convert it to String if I know the return type of getSize().
Anyway, this is the way that currently works for me.