No, you always need an app.yaml
file.
The README.md file on the DrEdit for PHP GitHub repository does appear to be a little confusing, it appears to be a Google Drive application (meaning it demonstrates interaction with the Drive API) that is written in pure PHP. Even though the first line of the setup instructions tell you to create an App Engine app, further down it tells you to copy the source to a folder on your web server, and does not mention anywhere about an app.yaml file.
There is no reason why you could not run it on App Engine though, you will just need to create an appropiate app.yaml
file. I have not tested it but something like this may work:
application: replace-with-your-app-id
version: 1
runtime: php
api_version: 1
threadsafe: yes
handlers:
- url: /(.+\.php)$
script: \1