This room should have been cut back ~10-15 sq. ft. and had its entrance in the hallway next to the top of the stairs. There are so many things wrong with this. Not to mention the obvious "you can step outside and fall" issue, imagine trying to close the door while entering the room and slipping. Imagine casually walking up the stairs when you're suddenly hit in the face with a door. Imagine the slammed toes when someone coming up the stairs closes the door so they can keep climbing steps. This is a hazard for people, pets, robot vacuums, and inanimate objects passing through the stairway or doorway. Hell, even things falling down the stairs can get caught between the door and the stairs and create an additional hazard. How do you egress out of the door and go downstairs in the event of a fire? I don't even know where to begin with this.
This would lead to slapstick levels of injuries. You could open the door, smack someone in the face, who then falls down the stairs, then you go to close the door and hit someone in the face trying to go down the stairs, who then themselves falls down the stairs....
EDIT: Shit. I'm not done. Opening the door creates a blockade preventing everyone upstairs from exiting the house through the stairway. Opening the door too far would rip the hinges from the door. Just standing in the stairway using your keys would lead to standing on completely uneven flooring. Imagine trying to unlock this door to enter the room while drunk. Ever get your shirt caught on the doorknob? What happens when you open the door and have a piece of clothing or a strap wrapped around the knob?