William Walker Marston was born in 1822, and would spend his career as a gunsmith and gunmaker in New York City. He produced a wide variety of firearms, including pepperboxes, multi-barrel derringers, percussion revolvers, and the breechloading single-shot pistol which we are looking at in this video.
This pistol is based on an 1852 patent Marston received for a cartridge which used a heavy paper or cardboard case and a leather base pad. That leather pad appears to have been intended as a self-clean bore wipe, which would be remain in the chamber when fired and then be pushed down the bore by the subsequent round. About 1,000 of these pistols were made, in a variety of barrel lengths (from 4” to 8”) and in all three popular calibers (.31, .36, and .44). While the cartridge was a nice improvement over a muzzleloading design, it was apparently not practical or innovative enough to become a real commercial success compared to the other types of combustible cartridges appearing on the market in the 1850s.
The tang sight on this pistol is rather interesting, as it seems to be usable only if the pistol is held very close to the eye. This suggests to me the use of a simple wire stock, although there is no evidence of such a thing being fitted to the gun.