Well, the answer is right there in the law. The facitilty must provide you with a place to store your weapon before entering the casino proper, which is where the gaming will take place. Restaurants, etc, are not included, unless they are on the actual boat.
If they are giving you a line of BS, ask to speak with the Gaming Commission Agent on duty. Also, print and take with you a copy of the law.
Edit: Ooops, sorry missed the part about the horse tracks. I am not sure who regulates horse tracks, but I do know that they usually have a different set of rules for them, as they are a different class of gaming.
Horse tracks work off of pari-mutual systems, meaning that you are not betting against the track itself, but rather against a pool of the wagers. The track takes a cut of the pool for its profit. This is commonly referred to as Class 2 gaming, from the defination provided in the IGRA.
Casinos are different. In a casino, you are betting directly against the casino itself. The casino makes its profit directly from the losses of the player, and creates these losses by a mathematical advantage in the games it offers. This is known as Class 3 gaming, and is more heavily regulated, to prevent fraud on the part of the casino.