Can you get rid of a president who does nothing for the club?

If the president does not load the game in 30 days, the game will replace him/her with another officer or player. Beyond that, there is no way to remove a president who won't step down. Your only other alternative is to ask members to join you in a new club that you start yourself.

If a president can’t play for an extended period of time, they should step down to an officer role and let someone else take the president seat for a while. We are in this situation right now - our president hasn’t done anything as a team leader for nearly 3 months and her last time in the lounge was about 6 weeks ago. But she must be loading the game at least once a month in order to stay in an active player state, since she’s still president, Wooga hasn’t replaced her. She’s not being fair to the rest of her team. It’s left a vacuum.

Start another team! This one is hers. She named it, she may be experiencing difficulties, but, on the other hand, she may not like the team dynamic, and is passively absenting herself. I would at the very least ask.