The game has no NTR, as at no point does the protagonist experience a situation where his romantic interest is taken away from him or cheats on him with someone else. Netorare involves an emotional loss for the protagonist due to the infidelity of a partner or someone he is interested in, which does not happen here.
What this game has, rather, is a protagonist with a harem. All relationships revolve around him, and there are no situations where the girls have encounters with other characters. The club you refer to is just a context within the story, but it does not imply that there is NTR in the game.
If you were expecting something different, I'm sorry for the confusion, but the story is centered on the protagonist and his relationship with the girls.