Hello Grant,
How did you deploy your app and to which environment? Your attached app.yaml does not seem to present itself in yaml format, and contains a log excerpt. Do you want to deploy to the App Engine environment, or to an instance of Compute Engine?
If your plan to deploy your app in the App Engine environment, you may have a look at the "Deploying a PHP App"
online guide.
By contrast, if your intention is to deploy to an instance of Compute Engine, you may check the "Running the PHP Bookshelf on Compute Engine"
example, quite useful as replete with deployment details.