The fog effect comes from Unity itself (or you can enable fog using a custom shader too),
and Vuforia does not play a direct role with it.
the camera video background image is a flat 2D image, of course, which comes from the device (phone/tablet) camera;
as such it does not contain any 3D / depth information;
as such, it is rendered as a flat background plane (in Unity, this is a rectangular plane mesh positioned at some distance from the Unity Camera);
so, when you enable a fog effect, all the pixels in the video bakcground image will be rendered at the same depth (i.e. same distance from the viewer), thus resulting all in the same fog intensity; this is probably the effect you are seeing, i.e. a sort of gray-ish plane, not a realistic fog effect.
To solve this, you would need to have a Depth Camera or sensor, which also provides the distance of each pixel from the camera (and you would need to have a software that can read such depth information and combine it with the RGB color image to produce the realisctic effect in the fog shader).