Unfortunately, the newspaper article does not go into the facts. In most states the trespassers' must show due diligence in attempting to contact the property owner, the sign does not have to contain the owner's phone number, address, or name. On the other hand as the property owner he should not have made contact with the trespassers' without a law enforcement official.
As an over-the-top dog lover; I would have requested a pound of flesh. My choice on location.
Be careful with righteous demands for a pound of flesh. I'm not sure about the laws in Arkansas, but Texas doesn't necessarily protect a landowner's right to be unreasonable... Which is exactly what shooting a leashed dog that a trespasser, probably in good-faith, recovered would be.