Original resolution notes:
This is by design. The project has shadows disabled under project settings.
To enable shadows, follow these steps:
Open the Project Settings window (Edit > Project Settings)
Open the Quality tab in the side bar
Note that the checkboxes next to the "Very Low" quality level are green - these are the active ones for the current platform.
Either scroll down to the "Shadows" dropdown, and change it from "Disable Shadows" to "Hard and Soft Shadows", or use the small arrows at the top of the Quality tab to change the currently active quality level to something more appropriate.
Addendum:
We'll consider improving the UX in this area, potentially adding a warning about missing shadows on low quality settings. This will be tracked seperately.