Since I don't have a 360 myself, I will post all the info I have right now to help you guys out :
The player is Flash 6 / 7. ActionScript 1 and 2 run on both. zlib compression is very common on Flash files, if not always (there's an option in the Flash IDE to turn it off, but that's not really relevant.)
The Player on the xbox is a custom build player. This means it might or might not have certain features the Flash players 6/7 do have. For instance using webcam features might or might not be implemented for specific reasons.
One thing which is for sure is that most "special" implementations of the MM Flash Player have hooks build in to talk to the host machine/os. On Flash Lite fscommand / fscommand2 is the method used to hook to the hosting platform (phones,mostly).
On the Xbox 360 Flash Player this is implemented through fscommands, aswell as through the getURL method, which is normally used to call a http page. This implementation is pretty weird and seems very hackish... I've compiled a little list of fscommands and getURLs possible :
getURL("FSCommand:LeaderBoardGameMode", GameMode); // XBOX LIVE/ARCADE Method
getURL("FSCommand:LeaderBoardSortOrder", SortOrder); // XBOX LIVE/ARCADE Method
getURL("FSCommand:LeaderBoardQuery", LeaderBoardSelected); // XBOX LIVE/ARCADE Method
getURL("FSCommand:LeaderBoardGameMode", GameMode);// XBOX LIVE/ARCADE Method
getURL("FSCommand:ShowGamercard", index); // XBOX LIVE/ARCADE Method
getURL("FSCommand:Presence", xml); //

?
getURL("FSCommand:DifficultyContext", xml); // XBOX Settings call ?
getURL("FSCommand:WriteStats", xml); //Writes an xml to the os ?

getURL("FSCommand:SaveSettings", xml); //saves an xml to the os ?

getURL("FSCommand:SoundFX", _loc2._Level_sfx); //Tells the os to play a sound ?
getURL("FSCommand:MusicVolume", _loc2._Level_music); //Changes volume on os ?
getURL("FSCommand:SaveGame", str); //
getURL("FSCommand:FileIOReadHeader", text); //Reads utf8 text from file
getURL("FSCommand:FileIOReadBody", text); //Reads utf8 text from file
getURL("FSCommand:FileIOWriteHeader", text); //writes utf8 text to file
getURL("FSCommand:FileIOWriteBody", text);//writes utf8 text to file
getURL("FSCommand:FileIOButton", text);//?

fscommand("LoadSettings", "settings");
fscommand("LoadGame");
fscommand("SessionReady", "true");
fscommand("TerminateGame", "<data><exit v=\"UserButton\"/></data>"); //Exiting the player?
These 2 geturls interrestl me most :
getURL("FSCommand:FileIOWriteHeader", text);
getURL("FSCommand:FileIOWriteBody", text);