The docs don’t cover this, but [the steps in this post][link] got it working for me:
1. Install composer `apt-get install composer`
2. Run `composer update` from the `extensions/Mailgun` folder
3. Run `php maintainence/rebuildLocalizationCache.php` from the main mediawiki folder.
Running your own services get you into all sorts of fun trouble like this.
[link]: https://phabricator.wikimedia.org/T144143 “Mailgun extension producing PHP Fatal Error about dependency Guzzle6”