The language on the sign seems to apply to law enforcement with concealed weapons also. Am I missing something?
My non-guaranteed opinion that isn't legal advice:
In English, sure, but legally, no, I don't think so.
Legally speaking, the only portion that really carries legal weight for CHL holders is the portion in red, which is the text required by law to prohibit CHL holders from carrying concealed on the property.
You could maybe argue that the portion in blue legally prohibits the carry of non-handgun firearms onto the property or beyond the sign. I don't know what the law or case law is on that particular issue..
The portion in black, I think, is factually incorrect. I'm assuming that what it is referencing is the section of code imposed on businesses with alcohol licenses that requires them to post a sign with text similar to that on the sign shown in the OP, but there is actually no law which prohibits the possession of a firearm on such properties. Actually what happens, is that the TABC attempts to overstep their lawful authority to prohibit firearms on such properties by forcing the businesses to prohibit by policy firearms on the property. While there is no law prohibiting a person from entering the property licensed to sell alcohol with a firearm, if the business knowingly allows that person to enter the property with a firearm they're subject to having their license revoked. Thus, as mentioned, the TABC is forcing businesses to enact policies which the TABC has no authority to enact themselves via the law.