I’ve clicked everywhere and had colleagues do the same, we cannot find the famous Delete Project option anywhere. And this is true for every project we have.
The words ‘delete’ and ‘remove’ don’t appear anywhere in the Edit Project page (even in the html the only occurrence of ‘delete’ has to do with sign_out).
In Gitlab 8.14.3 under Edit Project at the very bottom is a button for “Remove Project”. If you do not see that button you probably have a permission issue.