Really more of anachronistic 19th/20th century century jest. There are two components here. The handgun and the cartridge.
The your of handgun depicted is called a Derringer, which is typically a small, concealable gun that typically fires 2 shots before requiring reloading. Generally, Derringers fire small calibers because even something like a full 9mm will cause substantial recoil when there is no semi-automatic action or mass to absorb some of it. We'll come back to the particular Derringer shortly.
The .45-70 is a copper-cased, centerfire rifle cartridge developed for the US military in the late 19th century. The full classification of the original load being .45-70-405. This meant a .45 caliber (11.4mm) nominal bore diameter, 70 grains (4.54g) of black powder, and a 405 grain (26.25g) projectile. At the time of its adoption, it was recorded as having an effective lethal range of 1,000yds (910m). In 1879, a 500 grain projectile variant was developed with a legal range of 3,500yds (3,200m) - just to repeat this craziness, in 1879, the US military created a blackpowder rifle round capable of causing lethal injuries to those 3.2km away.
In modern times, the .45-70-405 is considered sufficient to hunt all big game in North America, including grizzlies and polar bears.
Now, back to that firearm. It appears to be an American Derringer Model M-4 Alaskan Survival. I highly doubt that any of the designers for a moment thought "a .45-70 Derringer is a good idea" and instead likely made it for novelty or to see if it could be done. I found some fun data on the M-4. It has a 4.1" (104mm) barrel length and, firing a 300 grain projectile, exerts 76.18 ft•lbs (103.29 joules) of recoil energy on its user. By compare, a similarly sized Glock 19 9mm firing a 124 grain projectile exerts 5.77 ft•lbs (7.83 joules) and the iconic Magnum Research Desert Eagle in .50AE only exerts 25.46 ft•lbs (34.52 joules) with a 300 grain projectile. So, the risk of injury to the operator is likely rather high and the manufacture and sale is likely rather irresponsible.