Why do No Tail Rotor (NOTAR) helicopters use an enclosed variable pitch fan?
They use a shrouded fan because these use less power than a jet for generating the same thrust. I could find a reference in Principles of Helicopter Aerodynamics by J. Gordon Leishman: he states that using jet exhaust for anti-torque required high power and that directional sensitivity was poor. 


Hiller Aircraft made a tailless prototype. 
The Nord Norelfe was constructed in 1954 and was used for the Aerotecnica AC-14 mentioned in the OP. 
The design was tested in the Cierva-Weir W-9




The reference to high power would refer to the generic issue with jets providing thrust: it costs less power to accelerate a higher volume of air to a lowish velocity (like a propeller does) than to accelerate a lowish volume of air to a higher velocity (like a jet exhaust does).