GMR experiences a lot of turn loading issues. Some games will be smooth as silk for some players, and require finagling for others. There are differnt methods that work for some people better than others. For me, I can usually get almost anything to load if I go load up a single-player game, play a few rounds, and then quoit back to the main menu, and try to load the GMR game again. Don't know how it works, but it usually does.
For some people, they have to run civ in different DX modes for different games. Some have to use the "legacy" download mode in the GMR client.
Try a few things, and if it still doesn't work, I'll revert it, and see if the previous player uploaded a corrupted save, if you still can't get it loaded after that, talk to GMR support. They're very helpful.