It appears the main issue is just that the menu item doesn’t show when you try to view it in the wp-admin area. I found the direct link to the page within the code of the plugin. If you ‘network activate’ the plugin and then go to one of your sites dashboard and enter a URL like this one: https://sub.network.com/wp-admin/plugins.php?page=manage_invites&action=view
Then it shows the pages needed to generate codes and other things. I hope this helps as a workaround for some at least until the plugin gets updated.
It’s been working for me so far.