Running lights do not need any type of load resistors or anything else to let them work.
It is only the turn signals that need the load resistors to get the flash rate correct. (unless you modify the flasher).
So if you think about it, when the turn signal is lit is the only time that the load resistor is pulling power. A turn signal when being used is only on 50% of the time it is being used.
It is very rare to ever have a turn signal on for more than 1 minute, the auto cancel tries to turn them off after just 15 seconds. So for turn signals it really does not make any significant power savings to have LEDs vs incandescents, BUT the amount of time the a turn signal is actually illuminated is very small compared to the amount of time that a running light is illuminated. This is where the power savings really are. Especially if you have a LOT of running lights that can be converted to LED.
Power saving is not the only reason to have LEDs, A good quality LED is brighter than the incandescent it replaces. The LED turn signal with its instant on and instant off makes it more noticeable than an incandescent of equal brightness. These are both desirable objectives.