The date field format is only used to display and edit the date in the field itself. After you click save, the date is always converted to YYYY-MM-DD to make sure it can be parsed in your templates. The structure field then fetches the actual value of the field, which has the wrong format.
I think the problem is that the format is only there to display the content while it is always saved to file in the same format no matter what format you define. And the entry in a structure field just takes the format from how it is saved to file. That could probably only be changed if the entry field had options to define the date format.