This could probably hacked up, but it would require a fair amount of code to do. I don't know the details upfront, but this is the approach I'de use, since you say you've dabbled in code.
1) Capture the screen data using code.
2) Transform the bitmap data into text (using Base64).
3) Send that text to a web server using an HTTP request, which in turn can perform the magic send that job off to a printer.
There may be a way to do this directly from the game alone, but the web-based approach is a more surefire way.