A recent update has introduced the ability to delete a file whilst it is open, here's how to do it.
Until now the only way to delete a Google format file from Google Drive was via the file listing inside of Google Drive. One drawback with this was the confusion over whether users could delete a file they did not own (they can't). With this new feature, that concern is removed - if the file is not owned by you the option to "Bin" is greyed out.
To delete a file that you have open, click on the File menu and select Move to Bin.
We think this is an easier and safer way for users to delete files, try it out and let us know what you think. This option is only available on Google format files - Docs, Sheets and Slides.