No, it's to specify to which of the two people in the pointy end one is referring.
The first sentence of the quote already establishes that:
"The captain has been with Southwest for almost 13 years and has been a captain for six of those years."
In the remainder of the quote, no confusion whatsoever would have arisen from the use, as is customary in English, of the personal pronoun he/she in relation to the same subject:
"[He/She] has over 12,000 total flight hours, over 7,000 of which are as pilot-in-command. In 737s, [he/she] has over 7,900 hours, with more than 2,600 as the pilot-in-command."
Avoiding the use of "he" or "she" was clearly intended to obscure the gender of the subject.