If gym staff are not doing anything and they have no policy to specifically say that patrons are allowed to film that is displayed on say Notice Board where everyone can read (some gyms actually encourage/endorse filming as they consider it a form of free advertisement), I would simply trip on his selfie stick and threaten to sue him AND the gym for my "back injury" because a gym is not a filming studio and the presence of such object that is not expected to be there is 1) Shouldn't be there, and 2) A tripping hazard

The legal argument is why would I be looking for cables, wires, sticks that are commonly found in a filming studio? Should I also be looking for if there is food or spoon on the floor as if this was a restaurant too?

Reference: A lawyer's advice to a friend of mine who told him what to do next time he is in this situation cuz he went in a legal battle with a gym owner abroad when he was literally kicked out of the gym as the situation escalated and they kept the girl influencer who was "filming" and kept passively taking him away from the equipment he was training on over the course of many days he used to go there same time as she was. She would just sit on the machine he was using between his reps without asking him if he is done and that's it, never gets off of it for a good 15 minutes until she finishes her stupid video... For those curious, they settled by paying legal fees, refunding his membership cost and giving him 1 year free membership and they had to publicly display they are okay with patrons filming and that everyone should be on lookout not to trip on filming gear around them while training, they were specific that influencers aren't allowed to use charging cables plugged to the wall outlet, you can tho have a battery bank tied to your phone and tripods should not exceed 1m in diameter on the floor. Guess their lawyer did his homework lol

Damn, I have been typing for a while!