Kirby Air Ride - "Kirby Melee"
As should be expected for a company with so many mascots, Nintendo has had a number of adaptations over the years. While these by default not part of Smash, several adaptation choices do sneak in (such as Ikue Ōtani's voice work as Pikachu, or a Zero Suit Samus costume from a Super Metroid commercial).
Despite casting such a long shadow over his creation, Sakurai's non-Smash relationship with Kirby ended with 2002's Kirby Air Ride. It was made around the same time as the Hoshi no Kirby anime (which Sakurai was also involved with, and likely more familiar to English speakers at Kirby: Right Back at Ya!), and both influenced the other extensively. They're products that are oddly both generically commercial and incredibly idiosyncratic, with very odd racing game design in the former and a slightly inexplicable satire of the Bush Administration in the latter.
I'm not actually sure whether the music in Air Ride is taken from the anime or vice versa (probably the former), but I doubt that anyone would have a problem with a little cross-adaptation pollination. This piece was placed in Air Ride's "Stadium Mode," but any cultural cache it has definitely comes more from the anime; it was the default "action" piece used during Kirby's transformations and comebacks. There are probably tracks from the anime that I'd rather see, but even more than the opening theme (and especially more than the English theme), it's probably the most iconic track from the show.