The sling is not used by the shooter in the picture because it is prohibited by the rules of the competition. In prone and seated you bet he's using that sling. In fact he's pulling on that sling so hard that an non-free floated barrel would change POI by at least an MOA (and that is with the front sight moving with the barrel). Total leverage is the same; but with a free floated barrel, only the upper receiver is bending, not the barrel and upper receiver. Admittedly the sling is least beneficial for standing, but it will still be an aid to stability, especially without the shooting coat and mitt.
The single point sling is a completely different animal, as 3 gun competition is completely different from CMP competition. I'm not as familiar with single point slings, but I perceive they are more for carrying and being quick to maneuver the gun than they are for precision marksmanship. They do help stabilize the positions somewhat when it is put to that use. Because the sling attaches to the back of the lower receiver only, sling tension is not as much of a concern, but competitors still prefer a free floated barrel. To start out in three gun you would probably find it's more important to understand your sights and bullet trajectory than to spend the extra money on upgrades to your equipment.
My recommendation is to learn the fundamentals of shooting. When you know how to make an ordinary rifle perform, then you will know a useful gadget from a well-marketed one.