Games are just an Internet page. Just HTML, CSS and Javascript No need of PHP/Node/ASP. Of course, you can use them but the communication with messenger is with Javascript. You can probably also uses VBScript or code an ActiveX but the easiest is to use JavaScript.
It’s simple, on each app, you send data to the other app with a function SendData and you receive data from the other app with a function Channel_OnDataReceived.
The documentation is still on Internet: Microsoft 365 documentation | Microsoft Learn
You can easily code an app and test it (just need two accounts): Microsoft 365 documentation | Microsoft Learn
You can download the files for the Tic Tac Toe: Tic_Tac_Toe_Classic_(10331358).zip (1.5 MB)
You can use jQuery 1.12 which is the last version to work with IE 7.
If you use the JK pacth ( Fixing Messenger's tabs to use the latest version of IE ), I think the version of IE will be different than 7 for games also.