I think the UAE company categories are to do with Emiratisation policies, number of employees, and how well a company follows MOL policies and UAE Labour Law - the category is for the company, not the employee. There are different fees for different category companies with Category A companies paying the lowest, and Category C companies paying the highest fees and charges at the Ministry of Labour (MOL).
Category A companies have at least 2% Emirati employees (UAE nationals).
Category B and Category C companies have fewer Emiratis employed and/or fewer total employees.
I've also seen reference to a bank guarantee payable by the company, but I don't know how up to date it is. I can't find confirmation on the MOL website.
Category A company no bank guarantee, or it's less than AED 3 million (which implies less than 1,000 employees if bank deposit is AED 3000 per employee)
Category B company bank guarantee is AED 3 million
Category C company bank guarantee is AED 5 million which implies minimum of about 1700 employees?
Check with the UAE Ministry of Labour
to confirm this information (and let us know if they say anything different