When Winn is listing Mon-El's main powers, they are identical to the initial powers of Superman in his earliest comics, right down to the "leap over a tall building in a single bound" phrase. Superman's ability to fly was invented by Fleischer Studios, who made a series of 17 "Superman" theatrical animated shorts from 1941 to 1943.
The concept of a superhero fight club was used for comedic effect to promote the CW's Arrowverse line of television shows. When Supergirl moved to the CW, an extended promo depicted her as eagerly joining a fight club run in the basement of Palmer Tech by the Flash and Green Arrow.
Mon El mentions War World, which in the comics is a planet used for televised fighting and made popular with the DC Comics character Mongul.