Designing serial robot communication software

    firstIntegerFromPC = atoi(strtokIndx); // my addition convert first part to an integer

Does that name REALLY mean anything to you?

    secondIntegerFromPC = atoi(strtokIndx);     // convert this part to an integer

That one?

void showParsedData() {
    Serial.print("Servo Number ");
    Serial.println(firstIntegerFromPC);
    Serial.print("Degrees movement ");
    Serial.println(secondIntegerFromPC);

It would make far more sense, to me, to print servoNumber and servoPosition.

Seems to work.

With those meaningless names, it is going to be hard to maintain.