A small public house has an office directly of the first-floor lounge. ASD in lounge. Extra office space is needed so the proposal is to remove the office and put in a flight of stairs to the second floor. Travel distance to the MOE on the first-floor is circa 18m.

If the stairs does not have a door at the top, can the arrangement still be considered an inner room?

Because the second-floor room is accessed directly from the stairs, it should still be considered an inner room.  The access is still dependant on the lounge, however the fact that there is ASD and visibility will make it an acceptable risk

The 'no door' or windows solution for an inner room is so the inner room occupier will quickly notice a fire developing in the access room - far less likely if the inner room is on another floor (until it's too late) so that would also make the 'no door' solution untenable to remove an unmitigated inner room. As Mike says you have AFD which is the more modern solution to the issue