Here is the wording for the exemption, and the relevant "Definitions" from the state code.
Sec. 802.005. EXEMPTION FOR CERTAIN PERSONS WHO BREED
SPECIAL PURPOSE DOGS.
(a) This section applies only to a dog bred
with the intent that it be used primarily for:
(1) herding livestock, as defined by
Section 1.003,
Agriculture Code, or other agricultural uses;
(2) hunting, including tracking, chasing, pointing,
flushing, or retrieving game; or
(3) competing in field trials, hunting tests, or
similar organized performance events.
(b) This chapter does not apply to a person to the extent the
person breeds dogs described by Subsection
(a) for personal use. A person described by this subsection
may conduct direct or indirect sales or exchanges in return for consideration
of dogs described by Subsection (a).
(c) Notwithstanding Subsection (b), a person described by
Subsection (b) may be subject to the requirements of this chapter
based on the person's activities with respect to animals other than
dogs that are bred and used as described by this section.
(d) Dogs described by Subsection (a) may not be counted for
purposes of determining the number of adult intact female animals
possessed by a person as described by Section 802.002(

.
Sec. 1.003. DEFINITIONS. In this code:(3) "Livestock" means cattle, horses, mules, asses, sheep, goats, llamas, alpacas, exotic livestock, including elk and elk hybrids, and hogs, unless otherwise defined.
SUBCHAPTER A. GENERAL PROVISIONSSec. 161.001. DEFINITIONS. chapter:(1) "Exotic livestock" means grass-eating or plant-eating, single-hooved or cloven-hooved mammals that are not indigenous to this state and are known as ungulates, including animals from the swine, horse, tapir, rhinoceros, elephant, deer, and antelope families.