Deuce is also fast with the other cowboy guns. Of the very top shooters Deuce is one that favors the Marlin whereas most use the '73 or '66. I'm pretty sure that rifle in the video is a .38-.357; it's the most popular chambering.
There is one category (B Western) in which the '73 or '66 are not allowed. The Marlin is always the top choice in that category since the other compliant rifles are nowhere near as good.
From memory I can't compare the stroke of the Marlin 1895 (which handles long cartridges like the .45-70) to the pistol caliber 1894. When you compare unmodified rifles, the Marlin has a shorter stroke than any of the Winchesters. For that reason the Marlin was heavily favored by the top shooters in the early years of cowboy action shooting. Then the gunsmiths figured out how to shorten the strokes on the '66s and '73s. There are different "generations" of short stroke kits out there so it depends on what work has been done on a rifle as to the length of the stroke. SASS passed a rule establishing a minimum stroke length but it may have been unnecessary because the shorter you make the stroke, the less mechanical advantage you have. The Winchester '92 (the rifle you most often see in old Western movies and TV shows, such as the one Chuck Connors wielded) cannot be short stroked although it can be slicked up a little.
Marlin's reputation took a beating after the company's acquisition by Remington. They actually shut down the line making 1894s to try to fix things. They are back in production and at the last SHOT show they re-introduced the Cowboy version with the octagon barrel. I wish Marlin much success. We need good Marlins in the sport. I think they are a good value if they work.