Nah you don't have to get the police involved in general. If you were involved in causing an accident in any way you are legally required to exchange your contact data with anyone else involved - in this case, the owner of the parked car. If you do that, you can each go your way without getting police involved. And nope, writing it on a note that you pin to the car doesn't suffice, you have to make sure to personally exchange the data so it is certain that it reaches the other person. With a parked car of course that can be an issue, you don't know where the owner is and they might not come to their car for days. So if you can't find the owner quickly, that's where you're required to call the police to file a report asap.
If you don't do that, it is "Fahrerflucht". That is a pretty broad term in German law that applies any sort of "unallowed withdrawal from the place of the accident", whether you've just intentionally t-boned the car of your fomer employer, ran over their garden gnomes and then drove away, or in this case accidentially scratched another car in the parking lot and drove off. That's why the headlines aren't technically wrong, it's all the same offense in German law.
PS: It's not "Fahrerflucht" if the driver can believably convey that they did not notice that they caused an accident.