I don't think it's meant to be any kind of real rifle around at that time. One of the character even said something about rifle's not being able to shoot that far.
Those were Sharps Borchardt 54 caliber single shot telescopic rifles. Yes, they did exist during the period depicted in the movie. Not sure if they had a reach of 800 yards, as shown in the film. Possibly....
It would make sense if they were Sharps –Borchradt, but they weren’t. They were “sporterized” Martini-Henrys, easily recognizable by indicator on the right side of receiver and hollowed upper surface of the breech-block:
Ruger's assertation that his use of telescopic sights on the rifles was the first time telescopes had been used on rifles, was in error. During the War of Northern Aggression, it was not uncommon to see sniper units utilizing accurate long-range rifles fitted with telescope sights.
I'd love to know how they propelled a heavy 54 caliber bullet at high velocity (800 yard accuracy) withour any discernible recoil!