First of all the question is, What is the Running basically? Why do we need the Running?
As far as I know, the basic purpose is to run the engine for a time until the required compression is achieved and all the internals clears/make their path.
For the first part, each piston should be having a thin carbon layer for best compression and it is best achieved running the car over Petrol or Diesel since they are best in producing Carbon rather than CNG producing less Carbon emission (almost 90% difference). Around 10-12 hours of running engine is the normal time period for running in case of the proper Carbon emission. In case of CNG, there is less Carbon, the running time of the engine is almost 20-24 hours or even more......
Secondly the internals clears/make their path, this is achieved in presence of engine oil, so it can be done by either fuel.(Petrol/Diesel/CNG).
As far as EFI technology is concerned, the engine must be continuously run until the cooling fan starts twice, that show that the ECU has learned the optimum parameters for running the engine according to the environment. Then by driving the car on a highway for around 30 minutes so that the ECU learns the driving habits. Once ECU learning process is complete, one can switch over to any fuel....