Most gyms are basically climate controlled for the most part. They weren't in my day, but they are nowadays. Whenever you make a permanent instal with any kinda plastic, PVC or some similar products, it wants to ever-so-slightly buckle from one fastener to the next. That's the nature of that kinda product. Unless you make a frame for it and have supports out the wazoo on the backside, you're likely to see it. Will it matter ?? That's up to you... or your customer. We make 100's of them a year for one customer alone. 3mm PVC 24" x 47" and we put them on with double sided tape and silicone. They don't mind the waviness. Any little yux in the wall will telegraph right through and to me it looks lousy, but PVC is a whole lot cheaper than gator. Their call.
Now, you might say, why am I doing it with tape and silicone and telling you to use screws ?? Mine are not even 8 sq ft at 3mm Yours are 24 sq ft and twice the thickness. Therefore you have at least 6 times the weight..... on a wall where kids and game-goers are all the time. Possible nightmare should something on your end fail. You need physical fasteners.