Seleccione lo mismo en la selección exterior. No puede acceder al nombre de alias en la misma consulta.
SELECT *, (CASE
WHEN articleNumber < 2 THEN 'Ama'
WHEN articleNumber < 5 THEN 'SemiAma'
WHEN articleNumber < 7 THEN 'Good'
WHEN articleNumber < 9 THEN 'Better'
WHEN articleNumber < 12 THEN 'Best'
ELSE 'Outstanding'
END) AS ranking
FROM(
SELECT registrationDate, (SELECT COUNT(*) FROM Articles WHERE Articles.userId = Users.userId) as articleNumber,
hobbies, etc...
FROM USERS
)x