As Information/Solution for other users of RunCPM on the Arduino Due:

There is a hardware-design-error on some Clones and some Revisions of the original
Arduino Due which prevents the correct use of the RX0-Pin (serial TTL-Port Receive-Pin)
while not using the USB-Programming-Port for accessing RunCPM on the Arduino Due.
See RX pin doesn't work

The solution is to use the serial port 1 = RX1 and TX1

For that you have to replace all occurrences of "Serial." with "Serial1."

After compiling/uploading the sketch RunCPM on the Arduno Due will work with projects like

PiGFX (Raspberry Pi as serial Terminal using USB-Keyboard)

and
ESPTerm (ESP8266):

see also (in german) the problem-description