Command-Line – What Are the Default $PATH Values

You mustn't use spaces around =, so it should look like this:

PATH=$PATH:/google_appengine

PATH is an environment variable, and therefor it 'defaults' or 'resets' when you change environment. See man sudoers for an explanation:

 env_reset       If set, sudo will reset the environment to only contain
                   the LOGNAME, SHELL, USER, USERNAME and the SUDO_* vari-
                   ables.  Any variables in the caller's environment that
                   match the env_keep and env_check lists are then added.
                   The default contents of the env_keep and env_check
                   lists are displayed when sudo is run by root with the
                   -V option.  If sudo was compiled with the SECURE_PATH
                   option, its value will be used for the PATH environment
                   variable.  This flag is on by default.

/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin

is the basic path without modifications. Different users will have different directories added to them for several reasons.

And the reasoning should be: root should never ever have more directories in its PATH than needed. Or the other way around: if root needs a file it should be in /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin. You do not play games as root. You do not use a desktop manager as root. A root is for admin tasks.

The wiki has some more information (amongst others which files are used to add to PATH): https://help.ubuntu.com/community/EnvironmentVariables