Here are the changes I made to the Google tutorial's app.yaml to fix the Wordpress install:
handlers:
- url: /wp-content/themes/fuse/library/css/custom.css.php
script: wordpress/wp-content/themes/fuse/library/css/custom.css.php
- url: /(.*\.(htm$|html$|css$|js$|ttf$|jpg$|jpeg$|otf$|woff$|svg$))
static_files: wordpress/\1
upload: wordpress/(.*\.(htm$|html$|css$|js$|ttf$|jpg$|jpeg$|otf$|woff$|svg$))
application_readable: true
- url: /wp-content/(.*\.(ico$|jpg$|png$|gif$|ttf$|jpeg$|htm$|html$|css$|js$|otf$|woff$|svg$))
static_files: wordpress/wp-content/\1
upload: wordpress/wp-content/(.*\.(ico$|jpg$|png$|gif$|ttf$|jpeg$|htm$|html$|css$|js$|otf$|woff$|svg$))
application_readable: true
- url: /(.*\.(ico$|jpg$|png$|gif$|ttf$|jpeg$|htm$|html$|css$|js$|otf$|woff$|svg$))
static_files: wordpress/\1
upload: wordpress/(.*\.(ico$|jpg$|png$|gif$|ttf$|jpeg$|htm$|html$|css$|js$|otf$|woff$|svg$))
I just enabled a few more types of static files (like otf and svg) and allowed a PHP file in the theme to run as a script rather than download as a static file.