It is likely that the Rock Club was created due to the fact that, at the time of the game's release, there were only seven TCG types— one short of the eight that were needed for a game that was like the core series Pokémon games, and, due to the additional double usage of the Grass-type by both the Grass Club and Science Club, the hesitance to use Colorless as a club type.
Gene can be challenged without having to meet a criterion set by the Club members or the Club Master himself, which is usually the standard practice among the other Clubs. Players who are able to beat Gene will receive the Rock Medal and two booster packs.
Chris from the Fighting Club is found here after Michael (also from the Fighting Club) is defeated. Once Chris is also defeated, he goes back to his club.
At the beginning of the game, the Rock Club is the only club to survive a takeover attempt by Team GR when Gene successfully defends the culb against GR-1. Any of the members are able to be battled from the beginning of the game and the prizes for winning, as well as the decks used, do not vary over the course of the game unlike the other clubs.