Why did Myanmar get removed from the list of countries on the international driving permit issued by the AAA sometime between 2016 and 2019?

The IDP (International Driving Permit) issued by the AAA would be according to the 1949 Geneva Convention on Road Traffic. Myanmar wasn't a party to that, but in June 2019, Myanmar ratified the 1968 Vienna Convention on Road Traffic, which replaced the Geneva convention. So an American IDP, based on the older, superseded treaty, would no longer be valid.

Note that the AAA form you're linking to says that the list is "as of May 2015."

From a report on the eight-day session of the tenth regular session of the Second Pyidaungsu Huttlaw by the Myanmar Digital News (back in December 2018):

[The] Hluttaw was explained by Union Minister for Transport and Communications U Thant Sin Maung on accession to Vienna Convention on Road Traffic 1968 and Vienna Convention on Road Signs and Signals 1968. The Union Minister explained that accession to the conventions would results in mutual recognition, support and speeding up of vehicles from convention member countries crossing from one country to another, reduce road and traffic hazards and ease international travel of vehicles.

As the traffic regulations in ASEAN Framework Agreement on the facilitation of Goods in Transit (AFAFGIT) is based on Vienna Convention on Road Traffic 1968 and Vienna Convention on Road Signs and Signals 1968, accession to the conventions will smoothen the implementation of ASEAN agreements said the Union Minister.

Furthermore, accession to the conventions will bring immediate recognition to International Driving Permit (IDP) issued by Road Transportation Administration Department that is not recognized internationally now. Due to this the Union Minister submitted to the Hluttaw to agree on accession to the conventions.

I don't see how keeping up an unofficial acceptance of the older treaty's IDP would have helped any of those goals. Certainly it wouldn't have helped mutual recognition one bit - does any signatory of the Geneva Convention but not of the Vienna Convention, even the US, accept Myanmar IDPs? I don't think so. I don't see why they should continue to accept the older treaty's IDPs when there's only dubious benefit to doing so, and when it certainly does not contribute to any of the aims stated above.