Here is scenario in which KIA wins 120 additional games (129 total) but does not necessarily finish in first place.

Here are the final standings in the scenario:
            Team	W	L	D	PCT	GB
             KIA	129	15	0	0.8958	0.0	See explanation of tie-breakers below.
              LG	129	15	0	0.8958	0.0	See explanation of tie-breakers below.
          Hanwha	93	51	0	0.6458	36.0
          Doosan	71	69	4	0.5071	56.0
             SSG	66	78	0	0.4583	63.0
              KT	61	79	4	0.4357	66.0
           Lotte	53	90	1	0.3706	75.5
          Kiwoom	48	92	4	0.3429	79.0
         Samsung	35	105	4	0.2500	92.0
              NC	26	117	1	0.1818	102.5

Explanation of Tie-breakers:
KIA and LG 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
              LG	17	4	0	123	0.810	0.0
           Lotte	12	10	1	121	0.545	5.5
          Hanwha	12	11	0	121	0.522	6.0
              KT	10	10	1	123	0.500	6.5
         Samsung	11	11	0	122	0.500	6.5
             SSG	9	10	0	125	0.474	7.0
          Doosan	9	11	0	124	0.450	7.5
             KIA	9	12	0	123	0.429	8.0
              NC	7	10	0	127	0.412	8.0
          Kiwoom	8	15	0	121	0.348	10.0

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	14	6	0	0	16	12	14	62
Hanwha	13	-	0	13	0	0	14	15	13	13	81
KIA	15	13	-	13	13	11	13	14	14	14	120
Kiwoom	0	0	0	-	15	0	13	12	0	0	40
KT	4	14	0	0	-	0	13	6	14	0	51
LG	13	13	3	13	14	-	14	14	13	15	112
Lotte	13	0	0	0	0	0	-	13	15	0	41
NC	0	0	0	0	7	0	0	-	0	12	19
Samsung	0	0	0	11	0	0	0	13	-	0	24
SSG	0	0	0	13	14	0	13	4	13	-	57
-----------------------------------------------------------------------------------
Losses	58	40	3	77	69	11	80	107	94	68

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

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	-	1	1	16	7	1	2	16	13	14	71
Hanwha	15	-	2	15	1	0	14	16	14	16	93
KIA	15	14	-	14	15	11	15	15	15	15	129
Kiwoom	0	1	2	-	16	1	13	13	0	2	48
KT	6	15	1	0	-	1	14	8	16	0	61
LG	15	16	5	15	15	-	16	16	15	16	129
Lotte	14	2	1	3	1	0	-	15	16	1	53
NC	0	0	1	2	8	0	1	-	2	12	26
Samsung	2	2	1	13	0	1	0	14	-	2	35
SSG	2	0	1	14	16	0	15	4	14	-	66
-----------------------------------------------------------------------------------
Losses	69	51	15	92	79	15	90	117	105	78

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