Here is scenario in which Kiwoom wins 115 additional games (128 total) but does not necessarily finish in first place.

Here are the final standings in the scenario:
            Team	W	L	D	PCT	GB
          Kiwoom	128	16	0	0.8889	0.0	See explanation of tie-breakers below.
             KIA	128	16	0	0.8889	0.0	See explanation of tie-breakers below.
          Doosan	87	55	2	0.6127	40.0
          Hanwha	77	64	3	0.5461	49.5
              KT	76	67	1	0.5315	51.5
         Samsung	51	92	1	0.3566	76.5
              NC	50	91	3	0.3546	76.5
             SSG	48	92	4	0.3429	78.0
              LG	43	98	3	0.3050	83.5
           Lotte	23	120	1	0.1608	104.5

Explanation of Tie-breakers:
KIA and Kiwoom 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
             KIA	20	7	0	117	0.741	0.0
              NC	16	11	0	117	0.593	4.0
         Samsung	15	12	1	116	0.556	5.0
             SSG	15	12	1	116	0.556	5.0
              LG	14	13	2	115	0.519	6.0
          Kiwoom	13	13	0	118	0.500	6.5
          Doosan	13	16	0	115	0.448	8.0
          Hanwha	11	16	0	117	0.407	9.0
              KT	10	18	1	115	0.357	10.5
           Lotte	8	17	1	118	0.320	11.0

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	0	13	13	13	11	13	11	74
Hanwha	13	-	0	0	10	14	13	3	13	0	66
KIA	13	13	-	3	13	13	14	13	13	13	108
Kiwoom	13	13	9	-	13	13	13	14	14	13	115
KT	0	0	0	0	-	13	13	13	14	13	66
LG	0	0	0	0	0	-	12	13	0	4	29
Lotte	0	1	0	0	0	1	-	13	0	0	15
NC	0	8	0	0	0	0	0	-	13	13	34
Samsung	0	0	0	0	0	10	13	0	-	13	36
SSG	0	13	0	0	0	8	12	0	0	-	33
-----------------------------------------------------------------------------------
Losses	39	48	9	3	49	85	103	80	80	80

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

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	-	2	1	2	15	15	14	14	13	11	87
Hanwha	14	-	0	0	13	15	14	4	14	3	77
KIA	15	16	-	7	15	16	16	15	14	14	128
Kiwoom	14	16	9	-	14	15	16	14	16	14	128
KT	1	3	1	2	-	14	13	14	14	14	76
LG	1	1	0	1	2	-	14	15	3	6	43
Lotte	2	2	0	0	2	2	-	14	0	1	23
NC	2	9	1	2	2	1	2	-	15	16	50
Samsung	3	2	2	0	2	12	16	1	-	13	51
SSG	3	13	2	2	2	8	15	0	3	-	48
-----------------------------------------------------------------------------------
Losses	55	64	16	16	67	98	120	91	92	92

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