Custom Menu options only show up for Network Admin account

I enabled custom menus in in functions.php for one of my multisite’s theme hoping that all users could customize the navigation menu of the site in question.

However, for some reason only I, the Network Admin, can access all of the custom post types and post tag options on the Edit Menu screen. Other regular admin accounts only see a limited selection of options on the left side.

Does anyone have any idea why this is happening? All I did was enable the custom menu features in functions.php and call wp_nav_menu() in my header.php file, no funny business. Do I need to change admin account privileges to include custom menus for multisites?