gistfile1.js

{"players": 
  {
    "gamertag": [ //gamertag would be set inside the loop through a variable, like "chapel" or "awesome"
      {
        "rating": 1234,
        "standing": 1
      }
    ],
    "chapel": [
      {
        "rating": 2345,
        "standing": 2
      }
    ]
  }
}

Ok i don't really know anything about data so i will assume here:

        var gamertag = player.PlayerDetail.gamertag,
                rating = player.Rating,
                standing = player.IndividualStandingWithNoRegardForTeams;

    var data = {"players": {gamertag: []}}; // Assumed!

    data.players.gamertag.push({"rating": rating, "standing": standing})