What I came to know is that the Qatar Ministry of Labour requires you to get cancelled any other GCC Resident visa (to work) before getting Qatari Resident visa (to work).
This I came to know from a friend of mine who was having Kuwait residency and was coming to Qatar for job, his company PRO requested to get his Kuwaiti's Residency cancelled before coming to Qatar so that he could apply for him Qatari Resident visa (to work).