If you choose to do mini-game she gain purity (which helps if you're aiming for that route) and increase her mood, which allows you to take better pictures, which generates more fans/subs/money. If you choose not to do it, you lower her mood but she gain corruption so if you have access to ways to regain that mood you basically have a easy corruption generator. I'm not sure what 4D chess like intellect you're using to think that it does nothing.
I DO have one request though. During that scene, you are presented with 4 options. All of the top 3 options have you do the mini-game, improve mood and gain purity with no real change. My request is that you have the 3rd option "I'll hep....but only if I get a good view while I work" could be changed to increase corruption without lowering mood. That way there's a reason to actually choose between the 3.