The Texas Board Of Professional Engineers licenses Professional Engineers. They do not license structural engineers. You could consider a PE license similar to an MD, or a medical license. An MD license authorizes the license holder to legally practice as a medical doctor.
Just because someone has an MD license, does not mean he can perform, say, heart surgery. He would not be granted permission at any hospital, but the MD license does not prohibit him or her from performing heart surgery. It is assumed that an MD will do competent work and not offer or perform work for which they are not qualified.
A PE license authorizes the holder to engage in the legal practice of engineering. It is assumed that they will not take projects for which they are not qualified.
The bottom line is that in Texas the is no Structural Engineering license per say. There is only a Texas Professional Engineer license.
So what then is a Texas Structural Professional Engineer? One way to answer that is that if they are listed on the roster of Texas Professional Engineers as Structural, then you can assume that they are qualified to practice structural engineering. When a prospective engineer applies for a license, he or she submits a detailed work history that has been verified by other Professional Engineers. The TBPE assigns each licensee to a branch of engineering based on their work history. Thus, if a PE is listed on the roster as structural, you can assume he or she is qualified to practice structural engineering.
On the other hand, if the engineer is shown on the roster as, say, mechanical, that does not mean they are not qualified to do structural work. It only means his work history was judged to be more supportive of mechanical than structural work at the time the license was granted.
This makes it sound as if the safe route would be to only refer Professional Engineers who are listed as structural on the TBPE roster on the web.