It would seem to me that this would, at minimum, be a civil case, but I would think you may still be able to get law enforcement involved. While it is true that in Texas a person has the right to kill a dog or coyote that is attacking livestock, I would have to say that if the officer who responded to the call documented in his report or recorded what this person said in regards to beating the dog to death with a pipe may be in your favor in a civil suit. You may want to look at;
Texas Penal Code sec. 42.092. Cruelty to Nonlivestock Animals -
(

“Torture” includes any act that causes unjustifiable pain or suffering.
(b) A person commits an offense if the person intentionally, knowingly, or recklessly:
(1) tortures an animal or in a cruel manner kills or causes serious bodily injury to an animal;
(d) It is a defense to prosecution under this section that:
1) the animal was discovered on the person's property in the act of or after injuring or killing the person's livestock animals or damaging the person's crops and that the person killed or injured the animal at the time of this discovery;
I would think this person would have to prove that your dog had injured or klilled one of his livestock animals first off, and second that it was justified it BEAT this animal to death. I would not think the law was written to include the killing of an animal in a cruel manner.
I think the advised given by Silverton Boar Dogs is on the mark "My advise to you is to go talk to the sheriff yourself, and then talk to the DA."
Sorry for your loss, and best of luck to you.