Looks like a bug... but here's a workaround:
- From the Structure page, click Add new child page.
- In the Add page window, enter a new page name (such as Foo) and click Update.
This adds the page Foo to your structure.
- You can now drag-drop pages into your structure, as expected, and the Save button appears (again, as expected).
- Save the structure.
- Delete the page you created in step 2.