Motion Sensor
 

Is the internal motion sensor an extra cost option?

Unless it was part of the "Boxster S - Sport Package" a $2235 option then no it wasn't, at least not on mine.

Under Comfort/Convenience there is standard feature called "Immobilizer Anti-Theft System", not sure if this is the motion sensor.

If the car had an alarm, it has the motion sensor. It is not part of the immobilizer package.