Just to play devil's advocate...
If the following is correct:
then their policy does not actually stipulate the method of carry.
The signs say that "All firearms must be checked at the service counter" and then underneath it says " This does not apply to concealed carry permit holders"
It simply says that anyone with a concealed carry permit is exempt from checking weapons, regardless of what method they have chosen to carry.
By comparison, if the sign/policy said:
then it would be a completely different story and only those with permits AND were legally carrying concealed would be exempt from checking firearms.
...This does not apply to concealed carry permit holders legally carrying concealed
Anyone open carrying by this definition would be required to check their firearms, or simply conceal before entering the store (assuming they had a concealed carry license).