Yes there is some sense to twisting the wires (minimizing the current-loop area.
The choke works by reducing the current fluctuations of the power supply, but it does not of course completely eliminate them. The twisted wires reduce the magnetic hum field generated by the remaining fluctuations.
The most important twisting is the heater power wires, where the fluctuating current is very high - 2.5 amps for the 6080 heater.
The dot usually signifies the start of the winding, standard practice it to use that with the highest AC voltage, i.e. the input of a filter choke. In this application the difference will be very tiny, so don't stress.