Yes the 737 does have nose wheel steering on the FO's side. It is controlled with the rudder pedals but the pedals have limited authority compared to the tiller on the capt's side. Both pilots have nose wheel steering.
Under favourable conditions, the aircraft can be turned 90deg to exit a runway with pedal control of the nose wheel and a given amount of differential thrust and/or and braking. If the FO did not do this, that's his choice and perfectly sound.
Some people get really excited about nothing.