In the world of precision marksmanship the term "Sniper Rifle" is relatively meaningless, as the proper definition of a "Sniper Rifle" is a "rifle that is used by a sniper." This means that Grandpa's lever action 30-30 is fully capable of being a "sniper rifle." Other definitions have come up, one that I like is, "a rifle chosen or built for accuracy for issue to trained marksmen." Snipers are trained to make a precision shot from a concealed position, with additional duties including scouting and serving as a forward observer for indirect fire.
The truth is that the "sniper rifle" doesn't have to be a rifle at all. If it can make the shot, then it can be used by a sniper.
The sport of long range hand gun has been dominated by the Thompson Contender for as long as I can remember. This is because of the it can handle traditional rifle cartridges (something that neither revolvers nor traditional semi auto pistols can do although some of the AR and AK pistols are exceptions) and does not bleed off any of the propellant gas between the chamber and the barrel like you would see in a revolver.
So having a highly accurate pistol that is capable of printing MOA or smaller groups at 200 to 400 meters is a pretty awesome capability. If I were "deer stalking" in the traditional manner a single shot pistol chambered for a suitable caliber (30-30 power level or up) then I would not feel undergunned at all.
On the other end of the spectrum, shotguns are almost universally equated with "short range" firearms. However the existence of rifled shotgun barrels in pump, break, semi auto, and bolt action configuration changed all of that. Now you can put three rounds inside an inch at 200 meters with a bolt gun using sabot slugs. Anyone who has seen a 175gr SMK shot at a typical vehicle windshield at the same distance will understand the usefulness of a "sniper shotgun" in that situation. It isn't that the slug will not deflect, it is just that it will deflect a lot less.
In the grand scheme of things of "all things sniper" the actual weapon system is not much of a concern. If the bullet can make it there with enough energy to be lethal, and you are good enough to put the bullet where you want it reliably, congratulations, some day soon the Brady Bunch and VPC will decry whatever it is you have; rifle, pistol, or shotgun, as a "long range murder weapon." Of course the weapon is nothing of the sort, I've yet to see any tool use itself.