Are you sure you see the exact message "Open Cargo doors" ?
You are not supposed to see that message with the PMDG 777, if the airplane is using the configuration that comes with GSX, the cargo doors should be referenced as "FWD Cargo" and "AFT Cargo", the same naming convention you see on the PMDG FMC.
This seems to indicate the airplane isn't using the internal configuration that comes with GSX, because of the following reasons:
1) You don't have the latest update to GSX code, which was published a couple of days after the 777-300 was released. To fix this, download and install the latest Stand-Alone Addon Manager for FSX.
OR
2) You tried to configure the airplane manually, and made some kind of mistake or have not configured the doors variables, which are custom for this airplane. To fix this, remove any GSX.CFG file you might have in one of these folders:
%APPDATA%\Virtuali\GSX\Airplanes\PMDG 777-300ER
FSX\Simobjects\Airplanes\PMDG 777-300ER