Well clearly every other dealer I've been to has these warranty administrators working out of the broom closet or something...
I know at the Mazda dealer I've bought some cars from the position was in an office away from the showroom floor. I only came to know much about the position as the local MB dealer was very small back then and offices were all right there.
I think the position is created when the volume of the service dept warrants (see what I did there?) Of course, a dealer can easily not spend the money on the position and have the service manager do it, but most large dealers I know now have such a person on staff as they can develop a relationship with the warranty authorization staff of the manufacturer, software involved, etc.
The first small dealers I knew to have this position were German makes because of the often very high cost of warranty repairs - a single denial could be very costly. They also do things like get try to get loaner/rental cars paid for by the manufacturer and other customer services. When a car is out of warranty, they can ask for goodwill money, a discount on a part, etc.
Some dealer groups have an admin dept that oversees several dealers and probably isn't located anywhere near a showroom floor.
Some warranty admins are also techs that verify diagnosis and ensure the proper repairs are being claimed.
I understand this is a very common and important job in the RV industry as RV makers are notorious for not paying up on warranty claims.