Go, MahJong, and Chess. Together?
I feel there are two major differences:


Go and chess are strictly strategic, whereas mahjong involves chance,
In go and chess, everyone has complete knowledge of the game at all times; in mahjong you don't know what your opponents have.


Mahjong is kinda of like poker or gin rummy in these ways; they more strongly depend on reading your opponent. So, in terms of core properties, I think mahjong is a different category of game to go and chess. Additionally, mahjong is more rules-heavy compared to the rules-light, strategy-rich go and chess.

That said, there's no reason not to play it in a club, as long as there are people who want to play it. Probably the best way to find out if it's suitable for your club is to try making the club, and offering mahjong as an option. If people don't want to play it or don't take it as seriously, then you can move your focus to the other games.