{"1":{"id":"1","game_id":"1"},"7":{"id":"7","game_id":"2"},"6":{"id":"6","game_id":"3"},"5":{"id":"5","game_id":"4"},"4":{"id":"4","game_id":"5"},"3":{"id":"3","game_id":"6"},"2":{"id":"2","game_id":"7"}}// преобразовываем строку JSON в массив
$array = json_decode('{"1":{"id":"1","game_id":"1"},"7":{"id":"7","game_id":"2"},"6":{"id":"6","game_id":"3"},"5":{"id":"5","game_id":"4"},"4":{"id":"4","game_id":"5"},"3":{"id":"3","game_id":"6"},"2":{"id":"2","game_id":"7"}}', true);
// получаем массив со значениями "id"
$id_array = array_column($array, 'id');
// объединяем значения в строку, разделенную запятыми
$id_string = implode(',', $id_array);
// выводим строку с id
echo $id_string;