What is the oath or sworn obligation of the retired officer to report the crime?
Any legal obligation to report a crime depends on whether or not his license is a permanent peace officer license.
Article 2.13 of the Texas Code of Criminal Procedure states that:
(a) It is the duty of every peace officer to preserve the peace within the officer's jurisdiction. To effect this purpose, the officer shall use all lawful means.
(b) The officer shall*:
(1) in every case authorized by the provisions of this Code, interfere without warrant to prevent or suppress crime;
(2) execute all lawful process issued to the officer by any magistrate or court;
(3) give notice to some magistrate of all offenses committed within the officer's jurisdiction, where the officer has good reason to believe there has been a violation of the penal law; and
(4) arrest offenders without warrant in every case where the officer is authorized by law, in order that they may be taken before the proper magistrate or court and be tried.
*NOTE the use of shall which IMO imposes a specific duty for a positive act, whereas in England and Wales the comparable legislation uses may which allows for some discretion and flexibility.
Article 2.12 of that Code defines a peace officer to include:
(1) sheriffs, their deputies, and those reserve deputies who hold a permanent peace officer license issued under Chapter 1701, Occupations Code;
(2) constables, deputy constables, and those reserve deputy constables who hold a permanent peace officer license issued under Chapter 1701, Occupations Code;
(3) marshals or police officers of an incorporated city, town, or village, and those reserve municipal police officers who hold a permanent peace officer license issued under Chapter 1701, Occupations Code...
Section 1701.307 of the Occupations Code does not expressly exclude the Texas Commission on Law Enforcement from issuing a permanent peace officer license to retired officers (but it does require the recipient to satisfy certain requirements such as minimum training standards, health checks etc). Unless he has such a license he does not appear to be under any legal obligation to report a misdemeanor.
As an aside, there are three mandatory reporting laws in Texas: when someone observes a felony resulting in serious injury or death; and when the victim of abuse or neglect is a child or vulnerable adult - but none appear relevant to the OP without confirmation.