Do NEC receptacle spacing rules apply to solid (half-wall) banisters
I would consider this a hallway and hallways less than 10' do not require an outlet NEC 210.52.H. This is not a room as defined by 210.52.A. 

The commentary for 210.52.a.3 says:


  any wall space that is unbroken along the floor line by doors, fireplaces, archways and similar openings must be included in the measurement. Room dividers such as bar type counters and railings are required to be in the 6' measurement. 


But this would be a hallway or landing. Local code may require an outlet at the landings but since it is not defined in NEC 210.52 there is no requirement for them in landings.