How do I delete an email in Gmail from the notification screen?
Yes - there is a setting you need to change.

The Notification bar's actions are based on what you have GMail set up to do when swiping away an email within the app.

To change it from Archive:

Open Gmail and go to Settings there change the Swiping conversation list from Archive/unlabel/delete to Always delete

This changed my Notification bar action from Archive to Delete