Penso che il problema riguardi il WHERE NOT
.prova con questa query:
$query = $em->createQuery(
'SELECT r ' .
'FROM AppBundle:Room r ' .
'WHERE r NOT IN ( ' .
'SELECT b.room ' .
'FROM AppBundle:Bookings b ' .
'WHERE ' .
'b.check_out < :check_in ' .
'OR ' .
'b.check_in > :check_out ' .
') ' .
'ORDER BY r.id'
)
->setParameter('check_in', $request->query->get('check-in'))
->setParameter('check_out', $request->query->get('check-out'));