The idea here is to connect the horizontal and vertical sync signals from the computer / laptop to the other monitors. However, the actual RGB data lines will be controlled by the Arduino / µC / ADC. You can see the pinouts for the VGA ports below.....

All that is happening with the software is that the Arduino or whatever is doing a digital conversion and then setting an output digital pin port to the lower 8 bits of the 10 bit data. That's all!