Posts 2 Posts: Display custom types connected to the same other custom type but with another connection

Maybe this could get you started:

function get_loser( $winner_id ) {
    global $post;
    $tournament = get_connected_id( $winner_id, 'won_final' );
    $loser  = get_connected_id( $tournament['ID'], 'lost_final' );

    return $loser;
}

function get_connected_id( $from_id, $connected_type ) {
    global $post;
    $result = array(
        'ID' => null,
        'post_title' => null,
    );

    if ( null === $from_id ) return $result;

    $connected = get_posts( array(
            'connected_type' => $connected_type,
            'connected_items' => $from_id,
            'nopaging' => true,
        ) 
    );
    if ( ! empty( $connected ) ) :
        $result['ID'] = $connected[0]->ID;
        $result['post_title'] = $connected[0]->post_title;
    endif;

    return $result;
}

Edit:
If you want all the losing players from all the tournaments that a certain player won, then I suggest doing something like this:

function get_losers( $winner_id ) {
    global $post;

    // get all tournaments won
    $tournaments = get_connected_id( $winner_id, 'won_final' );

    // this is the resulting array, init it.
    $all_losers = array();

    // Go through all the tournaments and find the loser
    foreach( $tournaments as $tournament ):
        $losers  = get_connected_id( $tournament->ID, 'lost_final' );
        foreach( $losers as $loser ) :
            // Here's a new loser, store the id and tournament id
            $new_loser = array();
            $new_loser['ID'] = $loser->ID;
            // add more fields if you like
            $new_loser['tournament_id'] = $tournament->ID;
            $all_losers[] = $new_loser;
        endforeach;
    endforeach;

    // We are done return the array of losers.
    return $all_losers;
}

function get_connected_id( $from_id, $connected_type ) {
    global $post;
    $result = array(
        'ID' => null,
        'post_title' => null,
    );

    if ( null === $from_id ) return $result;

    $connected = get_posts( array(
            'connected_type' => $connected_type,
            'connected_items' => $from_id,
            'nopaging' => true,
        ) 
    );

    return $connected;
}