We fight from the ground - we do not really have a separate groundfighting 'game'. It is movement that we center our study upon - to us, the ground is just another plane of movement.
Since we are an art born of military/combat, we choose not to stay on the ground for extended periods while tying up with an opponent - working five minute guards and holds (this is a good way to get stomped in real world). We move, hit, takedown and, generally, seek to get to feet again.
The 'work' Vladimir demonstrates on the groundfighting tapes seems alot more acrobatic than it really is, once you try it and learn the 'how'. It is, again, movement. We present a target to an opponent - then remove the target as the strike comes in. In certain ways, it is much easier to deal with an opponent from the grouind - once you know how to 'do the work'.