As you can see, the game is a throwback to the animated cartoons of the 20s and 30s, not to mention the classic (and sometimes insanely difficult) run-and-gun side-scrollers of the late 80s and early 90s.
The plot finds Cuphead (and Mugman when in co-op mode) losing a bet to the Devil and is forced to retrieve a particular item in order to repay the debt. Much of the game is based around large, continuous boss fights as opposed to having to run though long levels only to reach a short battle at the end.
The game was featured in the current issue of Game Informer (No. 263), exploring just how labor-intensive the project is. The development team is using actual hand-drawn animation as opposed to sprites or digital illustration and are even inking the character lines themselves (the one shortcut they admit to taking is using Photoshop to finish colors since trying to use paint would kill them). They've clearly studied many of the Fleischer shorts, early Disney cartoons, and Ub Iwerks in an effort to replicate the look and feel of those cartoons, even to the point of creating the grainy effect of the game being a long-lost cartoon itself. The article even notes six shorts the team recommend gamers watch in preparation, suggesting The Skeleton Dance (Walt Disney, 1929), Swing You Sinners (Fleischer Studios, 1930), Bimbo's Initiation (Fleischer Studios, 1931), Minnie The Moocher (Fleischer Studios, 1932), The Mad Doctor (Walt Disney, 1933), and Balloon Land (Ub Iwerks, 1935).