You asked, and now it's here! The ability to make multi-value dropdown list values required is now available. When creating a new field or editing an existing multi-value dropdown list, you will see the Required checkbox which will allow you to require users to fill out the field with the associated work item(s). Give it a try and let us know what you think!
You can find more information on multi-value dropdown lists here: Create and Customize Fields | CA Agile Central Help