I think, you will find that most rail doors are able to detect resistance against closing, if they detect appreciable resistance they may open again, (as are now required in electrically operated windows on cars) This obviously wasn't the case here, either an interlocking or sensing mechanism failed here, that told the driver all was OK to proceed.
Driver can or should only be able to proceed if signals from door sensors and interlocks satisfied a fail safe condition to proceed, if this condition was not met, the train may not have started to move, but there could have been an override button provided for instances when doors are playing up, or becomes faulty, then under those circumstances a driver may be able to get the train moving for instance to clear the path for other trains and take his faulty train to a rail workshop for repairs, ( I don't know but I am guessing, sure a train cannot be left standing at a station just cause of a door failure) or unless the faulty door had a manual override switch, where a driver would have to physically get down to the faulty door to trigger the override button, and manually shut the door locked before he could proceed)
if the driver did push an override button from his cab, and started to move without checking if it was a door playing up or a genuinely stuck passenger, then he may be found guilty of negligence.