CM does not work when delivery tier deployed as ROOT.war

Steps to reproduce:

1. Create a new archetype-based project (based on master, so archetype version 4.1.0-SNAPSHOT)
2. Follow the documentation to package the site as ROOT.war, including the rebuild and restart and the configuration in the console.
3. Open http://localhost:8080. It should work and show an empty white site with Essentials' default "Welcome to Hippo" message.
4. Login to the CMS and view the 'My Hippo Project' channel

Expected: it shows the same white site with the welcome message
Actual: it shows an "HTTP Status 404" page (see screenshot)