Here is scenario in which KT wins 36 additional games (98 total) but does not necessarily finish in first place.

Here are the final standings in the scenario:
            Team	W	L	D	PCT	GB
         Samsung	98	43	3	0.6950	0.0	See explanation of tie-breakers below.
              KT	98	43	3	0.6950	0.0	See explanation of tie-breakers below.
             KIA	73	67	4	0.5214	24.5
          Hanwha	71	70	3	0.5035	27.0
              LG	69	71	4	0.4929	28.5
          Doosan	68	71	5	0.4892	29.0
           Lotte	61	80	3	0.4326	37.0
             SSG	59	80	5	0.4245	38.0
              NC	54	87	3	0.3830	44.0
          Kiwoom	51	90	3	0.3617	47.0

Explanation of Tie-breakers:
KT and Samsung tie for first place and play a post-season game; the winner is awarded first place in the final standings and the loser is awarded second place.

To construct the scenario, we start with the current standings:
            Team	W	L	D	GL	PCT	GB
              KT	62	40	2	40	0.608	0.0
         Samsung	62	42	2	38	0.596	1.0
              LG	59	48	1	36	0.551	5.5
             KIA	57	48	2	37	0.543	6.5
          Doosan	56	48	4	36	0.538	7.0
          Hanwha	48	54	3	39	0.471	14.0
              NC	46	53	2	43	0.465	14.5
           Lotte	47	57	2	38	0.452	16.0
             SSG	44	62	4	34	0.415	20.0
          Kiwoom	40	69	2	33	0.367	25.5

The next two tables show, respectively, how many of their remaining games each team wins and ties against each of the other teams in the scenario:

					Scenario Additional Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	0	0	1	0	3	1	7	0	0	12
Hanwha	1	-	3	4	0	1	3	6	0	5	23
KIA	0	0	-	2	0	0	4	7	0	3	16
Kiwoom	4	0	2	-	0	0	2	3	0	0	11
KT	6	5	7	2	-	3	6	2	1	4	36
LG	1	5	4	0	0	-	0	0	0	0	10
Lotte	3	3	0	2	0	4	-	2	0	0	14
NC	0	0	0	1	0	5	0	-	0	2	8
Samsung	4	3	3	5	3	5	6	3	-	4	36
SSG	4	0	0	4	0	2	1	4	0	-	15
-----------------------------------------------------------------------------------
Losses	23	16	19	21	3	23	23	34	1	18

					Scenario Additional Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	1	1	0	1	1	0	0	1	0	1
Hanwha	1	-	0	1	0	0	0	0	0	0	0
KIA	1	0	-	0	0	1	1	0	0	1	2
Kiwoom	0	1	0	-	1	0	1	0	0	0	1
KT	1	0	0	1	-	0	0	0	1	0	1
LG	1	0	1	0	0	-	0	1	0	1	3
Lotte	0	0	1	1	0	0	-	0	0	1	1
NC	0	0	0	0	0	1	0	-	0	2	1
Samsung	1	0	0	0	1	0	0	0	-	0	1
SSG	0	0	1	0	0	1	1	2	0	-	1
-----------------------------------------------------------------------------------
Total	1	0	2	1	1	3	1	1	1	1

The next two tables show, respectively, how many total games each team wins and ties against each of the other teams in the scenario:

					Scenario Total Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	7	8	8	3	7	9	14	5	7	68
Hanwha	8	-	9	8	3	7	10	9	3	14	71
KIA	7	7	-	12	3	4	11	9	9	11	73
Kiwoom	8	7	4	-	3	5	4	9	4	7	51
KT	12	13	13	12	-	12	11	12	4	9	98
LG	8	9	11	10	4	-	7	5	5	9	69
Lotte	7	6	4	11	5	9	-	7	5	7	61
NC	2	7	7	7	4	10	9	-	3	5	54
Samsung	10	11	8	13	11	11	11	12	-	11	98
SSG	9	2	3	9	7	6	8	10	5	-	59
-----------------------------------------------------------------------------------
Losses	71	70	67	90	43	71	80	87	43	80

					Scenario Total Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	1	1	0	1	1	0	0	1	0	5
Hanwha	1	-	0	1	0	0	0	0	0	0	3
KIA	1	0	-	0	0	1	1	0	0	1	4
Kiwoom	0	1	0	-	1	0	1	0	0	0	3
KT	1	0	0	1	-	0	0	0	1	0	3
LG	1	0	1	0	0	-	0	1	0	1	4
Lotte	0	0	1	1	0	0	-	0	0	1	3
NC	0	0	0	0	0	1	0	-	0	2	3
Samsung	1	0	0	0	1	0	0	0	-	0	3
SSG	0	0	1	0	0	1	1	2	0	-	5
-----------------------------------------------------------------------------------
Total	5	3	4	3	3	4	3	3	3	5