SUMA con un pivote para calcular el puntaje general

Dado que está utilizando MySQL, para convertir los datos en columnas, deberá utilizar una función agregada con un CASE expresión:

SELECT callSign, 
    SUM(case when event = 'Bridge' then score else 0 end) as Bridge,
    SUM(case when event = 'PSA' then score else 0 end) as PSA,
    SUM(case when event = 'Amazing Race Planning' then score else 0 end) As AmazingRacePlanning,
    SUM(case when event = 'Team Analyst Exam' then score else 0 end) as TeamAnalystExam
FROM scores 
LEFT JOIN candidates 
    ON scores.candidateID=candidates.id 
WHERE candidateID IN (SELECT id 
                      FROM candidates 
                      WHERE assessmentID='1321') 
GROUP BY callSign

Si tiene un número desconocido de events , entonces tendrá que usar una declaración preparada para generar SQL dinámico:

SET @sql = NULL;
SELECT
  GROUP_CONCAT(DISTINCT
    CONCAT(
      'sum(CASE WHEN event = ''',
      event,
      ''' THEN score END) AS `',
      event, '`'
    )
  ) INTO @sql
FROM scores 
LEFT JOIN candidates 
    ON scores.candidateID=candidates.id;


SET @sql 
  = CONCAT('SELECT callSign, ', @sql, ' 
           FROM scores 
            LEFT JOIN candidates 
                ON scores.candidateID=candidates.id 
            WHERE candidateID IN (SELECT id 
                                  FROM candidates 
                                  WHERE assessmentID=''1321'') 
            GROUP BY callSign');

PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

Edite #1, si sus events se almacenan en una tabla separada, entonces puede usar lo siguiente para generar el resultado dinámico:

SET @sql = NULL;
SELECT
  GROUP_CONCAT(DISTINCT
    CONCAT(
      'sum(CASE WHEN event = ''',
      event,
      ''' THEN score END) AS `',
      event, '`'
    )
  ) INTO @sql
FROM events;



SET @sql 
  = CONCAT('SELECT callSign, ', @sql, ' 
           FROM scores 
            LEFT JOIN candidates 
                ON scores.candidateID=candidates.id 
            WHERE candidateID IN (SELECT id 
                                  FROM candidates 
                                  WHERE assessmentID=''1321'') 
            GROUP BY callSign');

PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

Consulte SQL Fiddle con demostración