It doesn't make a difference if he was a guest. From what you have stated, it sounds like they are liable. Before you resolve the situation, make sure you know the full extent and damages your son has suffered. If you did not make a report or let someone know when the accident happened, they may very well fight you on it saying that it did not happen. If you can, you need to go back and take some pictures and direct the manager to where the machine is so that both of you can view the problem. Then again someone else may have complained so that 24 hour already took care of it. Either way, I would not wait to get the evidence you need before it disappears.
I also would not worry about the waiver. He was hurt do to the direct negligence of 24 hour fitness, and I can almost always get around a waiver.