I can happily name most of the cartoons referenced here, though. Just by rote knowledge.
Farm level: "Little Red Hen"
Forest slime level: "Funny Little Bunnies"
First sky level: "Musicland"
Giant flower level: "Flowers and Trees"
Bug dancehall level: "Mr. Bug Goes To Town"
Candy dreamland level: "Candy Carnival"
Amusement park: Hard to tell but I think it's a shout out to Koko the Klown cartoons.
Arabian nights level: "Popeye Meets Ali-Baba"
Dragon sky level: Looks some aspects of "Water Babies" but maybe not.
Birdhouse sky level: "Pedro the Plane"
Bee level: "The Bears and the Bees"
Pirate level: Pretty much all Popeye cartoons.
Theater level: "Mickey's Mellerdrama" but the boss looks like Olive Oyl
Rat level: Gosh that rat looks like Mortimer Mouse.
Robot level: "The Mechanical Monsters"
Mermaid level: "King Neptune"
Ghost train: "Swing You Sinners"
Casino dicehead boss: That guy sure moves like Honest John from "Pinocchio", doesn't he?
The Devil: Sits on a throne like Hades in "The Goddess of Spring" but clearly one of his imps from that same cartoon. God, I love "The Goddess of Spring". And his final form looks like Chernobog from "Fantasia".
I am sort of the Rainman of pre-war cartoons, I think.