I'd say your in the right track, but instead of using the AND clause on your commented code, use OR.
if (usr_emp_type = 'Employee' OR usr_emp_type = 'Intern','Employee','Contractor') as [Nem Dimension]
So for each usr_emp_type, you'll have either 'Employee' or 'Contractor'.
Another way to do it is like so:
if (usr_emp_type = 'Employee' OR usr_emp_type = 'Intern',1,0) as [Employee Count],
if (usr_emp_type = 'Contractor' OR usr_emp_type = 'Customer',1,0) as [Contractor Count]
So on your charts, you can sum the created counters above.