From what you have said here, I would say the door does not need to be a fire door. The door opens onto an outside area so risk to other building users is virtually nil. However, in some such cases the door may still need to be self-closing fire door with smoke control where there is risk to life because an another property or walkway is located near to or directly above the door.
Furthermore, the fact that behind your door is just a staircase (going upwards) lessens the risk to life safety for others considerably.