How do I send an email from a non-gmail account using the appengine

That's a restriction of App Engine's mail API:

The sender address can be either the email address of a registered administrator for the application, or the email address of the current signed-in user (the user making the request that is sending the message).

If you've got Google Apps running on that domain, you should have (or be able to create) an @thatdomain.com email addresses that you can register as an administrator of the App Engine app in question, which will then let you send email "from" that address.