Well, if you'd read the link....
In order to recover a Moodle site you need a backup of the database (usually an SQL dump) and a copy of the files ("moodledata") area. You can download the actual Moodle code and any plugins again, so you don't need that (although it may be convenient).
Given that, you can copy "moodledata" somewhere, load up the database backup and point your config.php to these locations. That's (more or less) all there is to it.
So, it really rather depends what was in that "zip file". I assume it's the database backup and the moodledata backup.