Hi John,
Modern engine design and engineering has virtually eliminated the need for running in, and what is required is usually covered during the pre-installation engine test at the manufacturer - unless the manufacturer stipulates a running-in period.
So what was a formal running-in period has been replaced by a small set of fairly indeterminate things that need to be considered by the driver, such as the need to take care on new tyres, allowing the brake pads to bed-in before doing any heavy braking, etc.
By the time 500 miles are up, the brake pads should have conformed to the shape of the discs, the tyres should be clean, etc.
My car has a fairly large, high output diesel engine, coupled to an automatic gearbox - so I rarely use full throttle - preferring to let the engine and gearbox to stay at peak torque. So I guess I'm always driving the car like you once did to run an engine-in.
Robert