Is it possible for me to delete a failed Quest game? I can't find out how to.

Wrong forum. I'd try the General Discussions or the Site and Announcements feedback forum.

Why do you want to delete it, anyway? Is it really that bad, or does it just have a bad glitch?

If it is a bug, you can upload a new version of your game any time.

Otherwise, I think you would need to contact manowar, who runs the web player.