The host's specs are fine. If it was directly related to the specs it should affect single player, as well.
It appears to be something GPU / DirectX related...
Does Fake Fullscreen also help, or just Windowed?
The host can try resetting their graphics driver's 3D settings to default (right click an open area of the desktop to start the nvidia Control Panel).
A clean re-install of the graphics drivers could potentially help (see
here or
here, for example).
