do you think a "No Guns" sign would have deterred him? After all, the way the law is presented, a hotel employee would actually have to see him with a firearm, and order him to leave the premises. Not much deterrence there, it seems.

Platitudes and virtue signaling do nothing to reduce the number of shooting deaths.

Let’s try getting tough on people caught with illegal guns
Let’s send a clear message that crimes committed with guns are severely punished
Let’s get tough with straw purchases
Feel good legislation just allows people to shrug their shoulders and say’ I tried’

If the casino, or any business, does not want firearms on-premises, just clearly post such on the entrance and on their website. If citizens, legal gun owners or not, want to enter these establishments, they will leave firearms in the car. If they chose to patronize other businesses, that is just exercising free will. Nobody is forcing patronage at these businesses.
This is not unreasonable to RKBA and antis both. If you don't like the policy of that business don't spend your money there. This is not that complicated.

#1 is how you describe it. The sign is called a 30,06 and refers to the carry of concealed weapons.

#2 is called a 30.07 law and refers to openly carried weapons.

There is also the 51% law for restaurants and "bars". It says that if an establishment makes 51% or more of their income from the sale of alcohol, then no carry, concealed or open is allowed. This is enforced by the Texas liquor laws.