I am surprised that the punishment listed is all that happened to the officer from the agency, but it is about all that could be done under the law. Remember that not all states have the same laws.
Since I agree that the laws should apply to everyone equally, and I was curious why the officer was not charged further, I went and looked up South Carolina law on animal cruelty. Note that this was a quick search, so I might have missed something. SC requires that the cruel treatment be knowing or intentional. There was no law I found specifically mentioning being left in a hot car. I honestly do not think the officer intended the injury should happen. I don't think he did it knowingly either. I do think it was negligent, and might be reckless though I am not sure about the reckless part. There is a fine line in the law differing between negligence and reckless and I am not sure if it was crossed or not. A reckless act means the person disregarded a risk he was aware of that a reasonable person would not. A negligent act is one where the person ignored a risk a reasonable person should have been aware of. So, if I were a DA, I would probably have used negligence as the charge if the law allowed it.
To compare the law to Texas, for non-livestock animals (PC 42.092), Texas requires reckless conduct. For livestock (PC 42.09), we require intentional or knowing acts. In the case of an officer who leaves his dog in the car while he steps into the station to write a report, planning to return in a few minutes, I would say an injury would be negligent behavior. He should be aware of the uncertainty of when he would return to the car. I am unsure if it would rise to reckless or not. Most people who leave the dog in the car don't intend the dog to get hurt, but also don't plan on returning in a few minutes. Again, it is negligence, but I am unsure if it rises to reckless behavior.
So, I think the officer was treated appropriately in South Carolina and I am not sure anyone who left their dog in the car in Texas should be charged under our law. I am sure that if a department would charge a citizen then they should charge the officer also.