SELECT *
FROM `videos` AS `v` LEFT JOIN `videocategory` AS `vc` ON vc.id=v.id_videoevent and v.type=2  //категория
LEFT JOIN `typesport` AS `s1` ON s1.id = vc.id_sport
LEFT JOIN `videoevent` AS `ve` ON ve.id = v.id_videoevent and v.type = 1 //событие
LEFT JOIN `typeevent` AS `e` ON e.id = ve.id_liga
LEFT JOIN `typesport` AS `s` ON s.id=e.id_sport