How to make it appear as if the ground is moving?

Convoy uses a scrolling ground texture and the rock props are attached to trains that teleport back to the beginning.

Yeah, convoy makes the skybox camera move through an environment, so the background is moving (not the player) which gives the illusion of the player moving.
Decompile ctf_convoy or use no clip and look at the 3d skybox to learn it .

take any vtf and paste this into its vmt:

"LightmappedGeneric"
{
"$basetexture" "yourfolder/yourtexture"
"$surfaceprop" "rock or whatever"
"Proxies"
{
"TextureScroll"
{
"texturescrollvar" "$baseTextureTransform"
"texturescrollrate" 0.6
"texturescrollangle" 90
}
}
}

texturescrollrate controls the speed of the scroll (obviously) and texturescrollangle controls the direction of the scroll. You should just have it at 0 or 90