This page explains in detail the interactions between the Mario series and the Rally-X series.
Mario Kart Arcade GP[]
October 2005
One of Pac-Man and Ms. Pac-Man's exclusive items, unlocked by winning all cups in Grand Prix mode, is called "Rally-X" and is an actual car from the game.
Its description in the official game's site is: "Smoke appears. Spin out when hit".
It also returns in Mario Kart Arcade GP 2 along with all other items, and in Mario Kart Arcade GP DX as a generic item usable by any racer.
Mario Kart Arcade GP DX[]
July 25, 2013
The Rally-X car from the previous games returns as an item, but now also as an unlockable kart called X-Racer.
License[]
While published by Nintendo, the arcade Mario Kart games were produced by Namco, so they could freely include elements from Rally-X in the game.