Linked in this post are downloads to the official Messenger Activity SDK, which includes documentation for writing activities and games and an incomplete version of the Tic-Tac-Toe Classic game, and an unofficial Activity sandbox that was developed to allow for testing of Activities without requiring usage of the official clients, instead relying on browser technology. Sadly the sandbox only works on IE, though (especially if the Activity you plan to test is reliant on IE technology). The Activity sandbox I believe was developed by "TheBlasphemer" around 15 years ago (September 2005) and contains a complete version of Tic-Tac-Toe and a custom activity designed for the tool. Here are the notes for it copied from a forum post by the author themselves:

Currently it supports almost everything, except filetransfer, and the _NewEnum method of Users (how does it work anyway?)
To test your app in the sandbox youu will have to do some minor modifications:
First, do a simple search&replace replacing "window.external" with "GetExternal()"
Next, add the function GetExternal to your script, steal it from one of the added test-games.
Lastly, remove any unnecesarry headers, like doctype and meta stuff, somehow this f*cks up the script :P

Currently, all I've tested is a modified tictactoe, and joosts test (which is slightly bugged ;))

...

Things I still want to implement:
- Forcing 2packets/second
- measuring max datatraffic
- add packet delay

As stated by the author, the sandbox tool is unfinished and inelegant when it comes to how it emulates Activity functionality, so use at your own discretion.

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Official Messenger Activity documentation + Tic-Tac-Toe example: https://www.dropbox.com/s/t22kxpgsqsdcy0u/messengerActivitySDK.zip?dl=0
Unofficial Activity sandbox (unfinished, works on IE only): https://www.dropbox.com/s/pjgkppcnq7hije4/Sandbox.rar?dl=0