There is a mechanical lockout on Park if you are moving (faster than about 5mph), the lockout is what caused the grinding noise and shouldn't have caused any real damage.

Yep not the greatest thing to do but its not the end of the world. Just don't make a habit of it

I know that sound from past cars. The thought gives me the willies.
Are you sure its the same putting a car into park as us manual drivers putting the car into gear without pressing fully on the clutch? It seems like it could be more damaging.

Less damaging. The parts that are grinding in the AT case aren't the gears, just the park mechanism. Worst case would be if you did it repeatedly that you wouldn't have a park transmission lock anymore. The engineers think of people doing things like this and design the teeth on the park such that they cannot engage at speed.