I pretty much exclusively make my Gamestop purchases with a check card,and I've never been carded for anything short of an M-rated game. However, I'm not a member of the rewards program, and I never pre-order anything except for the Harry Potter books, and that series is over and completely unconnected to Gamestop. I doubt that Florida has stricter laws on this than California, since A.) it's a point of pride among our state politicians to be "friends of business" -- and indeed, our current governor is a corporate raider who financed his campaign with embezzled funds -- and B.) if your signature has rubbed off of the card, it's not uncommon for a clerk in any given store to check the signature on your driver's license instead, so at least in that situation, I doubt it's illegal.
What I really wanted to post here was man, that is one roomy Gamestop. Even the big ones around here are the size of an oversized walk in closet, and the small ones are the size of normal one. The store in the picture looked like it was closer to the size of a gas station convenience store, or even an FYE. I'm sure the camera angle played a part, but man do I wish the local Gamestops were that big.
Edit: I never trade games either; once it comes into my possession, it stays there forever. There is a good reason for Gamestop to run your card with system trade ins, which may extend to game trade-ins as well. Basically, the store is treated like a pawn shop under the law, at least in Florida, and they are required to take down serial numbers and hold the items they take in while they wait for any stolen property reports to come in. I know this because I went on a long, fruitless search to get a replacement for a used DS Lite that I got for Christmas thanks to a Black Friday sale, which unfortunately had a cracked hinge. Long story short, I never did get the stupid thing traded out for one that wasn't faulty, but I did learn a lot more than I ever wanted to know about how Gamestop handles trade-ins.