Odd, and almost unbelievable, the copilot, after coming to a stop, didn't set the brakes and move to the LH seat and taxi the aircraft to the gate.
Reminds me of a US wide body to be delivered to a UK airline with only LH seat steering tiller. The CAA requirements at the time (early 70s) were for both LH and RH tillers to be installed, so the aircraft had to be modified before delivery. One of the few CAA requirements/differences that made sense.
I do not believe that taxing into a cramped, very busy ramp to a gate with just one pilot in the cockpit would be a very wise idea. Also most likely against company operations specs.
No matter which seat they were in.