First lets talk about why F-Zero GX news is posted on a SEGA blog, if you didn’t already know the game was developed by Amusement Vision (SEGA AM4) the guys that did games like Super Monkey Ball and later Yakuza series. Did you also know that F-Zero GX used the Super Monkey Ball engine?
F-Zero AX is the name of the arcade version of the game, which was developed along side F-Zero GX for GameCube. Well, it happens that the full arcade version was hidden away on the Gamecube disc of F-Zero GX and if you have an Action Reply or Gameshark, you could online the game. You have to check out the Retro Collection lists of codes, that will get you started. Though as pointed out by some YouTube comments, there are subtle differences from the arcade version. Probably never completed and was scrapped as an unlockable?