**SHORT ANSWER**
It may depend on whether or not his license is a *permanent peace officer license*. 

**LONG ANSWER** 
Article 2.13 of the [Texas Code of Criminal Procedure](https://statutes.capitol.texas.gov/Docs/CR/htm/CR.2.htm) 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.
> 

<sub>*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.</sub>


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](https://statutes.capitol.texas.gov/Docs/OC/htm/OC.1701.htm#1701) 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 (training, health checks etc), so 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 two mandatory reporting laws in Texas: when [someone observes a felony](https://casetext.com/statute/texas-codes/penal-code/title-8-offenses-against-public-administration/chapter-38-obstructing-governmental-operation/section-38171-failure-to-report-felony#:~:text=Section%2038.171%20%2D%20Failure%20To%20Report%20Felony%20(a)%20A%20person,and%20(2)%20fails%20to%20immediately) resulting in serious injury or death; and when the victim of abuse or neglect is a [child](https://statutes.capitol.texas.gov/Docs/FA/htm/FA.261.htm) or [vulnerable adult](https://statutes.capitol.texas.gov/Docs/HR/htm/HR.48.htm) - but neither appear relevant to the OP without confirmation.