Targeting categories in custom fields

Have you tried using include/exclude?

$taxonomy     = 'game-type';...
$include="ANDROID ID IE: 1"

    $args = array(...
        include           => $include
    );

EDIT: vancoder is right: it should be…

   $taxonomy     = 'game-type';...
    $child_of="ANDROID ID IE: 1"

        $args = array(...
            child_of    => $child_of
    );

Where $child_of is the ID of your subcategory.