The message shows, that the extension / module is not correctly loaded for your webserver. So yes, this is a server side issue.
Please contact the support of your webhoster, especially as you’re using cPanel. They might be able to tell you whats wrong here and how to fix it.
Reason:
ownCloud would show “PHP module zip not installed.” not “Required PHP extension not found : zip” so this is something cPanel specific where people in here can’t help you with.