정렬 기준으로 created_dt 를 사용해야 하는데 중복이 가능하므로 유니크한 bno 를 정렬기준으로 추가해야 합니다.
예시 자료의 bno 순서가 거꾸로 된것이 아닌가 생각되네요?
최신 등록 글의 bno 가 더 크다고 가정하고 작성했습니다.

WITH t AS
(
SELECT 9 bno, '공지사항' category, '공지A' title, '공지내용A' content, 25 hits, '관리자' writer, '2019-01-05' created_dt, '2019-01-05' updated_dt
UNION ALL SELECT 8, '공지사항', '공지B', '공지내용B',  9, '관리자', '2019-01-04', '2019-01-04'
UNION ALL SELECT 7, '자료실'  , '자료A', '자료내용A', 10, '관리자', '2019-01-03', '2019-01-03'
UNION ALL SELECT 6, '문의'    , '문의A', '문의내용A',  2, '관리자', '2019-01-03', '2019-01-03'
UNION ALL SELECT 5, '문의'    , '문의B', '문의내용B',  4, '관리자', '2019-01-03', '2019-01-03'
UNION ALL SELECT 4, '자료실'  , '자료B', '자료내용B', 30, '관리자', '2019-01-02', '2019-01-02'
UNION ALL SELECT 3, '공지사항', '공지C', '공지내용C', 17, '관리자', '2019-01-02', '2019-01-02'
UNION ALL SELECT 2, '자료실'  , '자료C', '자료내용C',  6, '관리자', '2019-01-01', '2019-01-01'
UNION ALL SELECT 1, '문의'    , '문의C', '문의내용C',  3, '관리자', '2019-01-01', '2019-01-01'
)
-- 1. mySQL 도 8.0 부터는 분석함수 지원됩니다.
SELECT *
  FROM (SELECT a.*
             , ROW_NUMBER() OVER(PARTITION BY category ORDER BY created_dt DESC, bno DESC) rn
          FROM t a
        ) a
 WHERE rn <= 2
;
-- 2. @변수 사용
SELECT *
  FROM (SELECT a.*
             , @rn := CASE WHEN category != @category THEN 1 ELSE @rn + 1 END rn
             , @category := category x
          FROM t a
             , (SELECT @category := '', @rn := 0) b
         ORDER BY category, created_dt DESC, bno DESC
        ) a
 WHERE rn <= 2
;
-- 3. Self Join
SELECT a.*
     , COUNT(b.bno) + 1 rn
  FROM t a
  LEFT OUTER JOIN t b
    ON a.category = b.category
   AND ( (a.created_dt < b.created_dt) OR
         (a.created_dt = b.created_dt AND a.bno < b.bno) )
 GROUP BY a.bno
HAVING COUNT(b.bno) < 2
;
-- 4. Exists
 SELECT *
  FROM t a
 WHERE NOT EXISTS (SELECT 1
                     FROM t b
                    WHERE a.category = b.category
                      AND ( (a.created_dt < b.created_dt) OR
                            (a.created_dt = b.created_dt AND a.bno < b.bno) )
                      AND EXISTS (SELECT 1
                                    FROM t c
                                   WHERE b.category = c.category
                                     AND ( (b.created_dt < c.created_dt) OR
                                           (b.created_dt = c.created_dt AND b.bno < c.bno) )
                                  )
                   )
;
-- 5. 카테고리별 Limit, Union
(SELECT * FROM t WHERE category = '공지사항' ORDER BY created_dt DESC, bno DESC LIMIT 2)
UNION ALL (SELECT * FROM t WHERE category = '자료실' ORDER BY created_dt DESC, bno DESC LIMIT 2)
UNION ALL (SELECT * FROM t WHERE category = '문의'   ORDER BY created_dt DESC, bno DESC LIMIT 2)
;