Is anything incumbent upon me after I lightly struck a stationary car, which was unaffected, and then left the scene?

If the minor collision did not cause any damage to the vehicle that was hit, then you owe nothing. However, if it caused damage, even slight, then you must compensate the owner of the vehicle for it, unless they waive their right. If you can reach the owner of the vehicle and reconcile with them, then do so. Otherwise, estimate the amount of the damage and give it away in charity on their behalf.