I'm not familiar with an "important updates" setting. Taking a look at Group Policy, there's a setting for "Turn on recommended updates via Automatic Updates" that sounds close but I just looked at the prior screen shot and realized it probably corresponds to the "Give me recommended updates the same way I receive important updates" checkbox.
In the group policy editor, navigate to Computer Configuration -> Administrative Templates -> Windows Components -> Windows Update.
Select "Configure Automatic Updates" and provide a screenshot of that.
In the group policy editor, navigate to Computer Configuration -> Administrative Templates -> Windows Components -> Windows Update.
Select "Configure Automatic Updates".
Open the listbox below "Configure automatic updating" and provide a screenshot of that.
3 options under 'Important Updates'. Other two are "Install updates automatically (recommended)" and "Check for updates but let me choose whether to download and install them".