In Texas, can the owner of vehicle claim non traffic damages?

I am not certain what you mean by "non traffic damages".  If what you are asking about is damage to your vehicle caused by a means other than another car, then the answer is yes.  If you have auto insurance and carry comprehensive coverage on your policy, you are covered for such things as theft, vandalism, storm damage, rocks hitting your windshield on the highway, etc.  If you are asking whether or not you can make a claim against another party for damage caused by something other than a traffic accident, the answer is, it depends.  If your neighbor's tree falls on your car, for example, and the neighbor knew or should have known that the tree was sick and might fall, then yes, you have a claim.