This law concerns the licensing of abortion facilities. The only crime established under this definition of abortion is a misdemeanor, and the elements of the crime are:
Except as provided by Section 245.004, a person may not establish or operate an abortion facility in this state without an appropriate license issued under this chapter.
So the trivial answer to this question is "no, because this definition is not relevant to a person seeking an abortion." It might allow people to open clinics that terminate pregnancies of trans men, but I doubt that would succeed.
As to criminal prohibitions relating to the act of abortion itself, there does not seem to be a definition of abortion in the penal code, but rather there are various things such as a definition of "individual" that includes "unborn child." Still, there is gender-specific language such as (22.12):
This chapter does not apply to conduct charged as having been committed against an individual who is an unborn child if the conduct is: (1) committed by the mother of the unborn child; ...
I have no trouble believing that any court will easily find either that the person bearing the child is necessarily female or that it doesn't matter whether the person is female. Among other things, the Texas penal code includes this (1.05)
(a) The rule that a penal statute is to be strictly construed does not apply to this code. The provisions of this code shall be construed according to the fair import of their terms, to promote justice and effect the objectives of the code.
(b) Unless a different construction is required by the context, Sections 311.011, 311.012, 311.014, 311.015, and 311.021 through 311.032 of Chapter 311, Government Code (Code Construction Act), apply to the construction of this code.
And, whaddya know, 311.012(c) says "Words of one gender include the other genders." There is no reason to think that prosector or judge would interpret a provision intended to protect the life of an "unborn child" so as to render its effectiveness dependent on the gender of the person bearing the child.