This would be my way of solving, using pd.melt and groupby:
import pandas as pd
data = {
    ('player_1', 'name'): ['Juggernaut'] * 20 + ['Pudge'] * 20,
    ('player_1', 'kills'): range(40),
    ('player_2', 'name'): ['Clinkz'] * 20 + ['Axe'] * 20,
    ('player_2', 'kills'): range(1,41),
    ('player_3', 'name'): ['Tiny'] * 20 + ['Snapfire'] * 20,
    ('player_3', 'kills'): range(2,42),
    ('player_4','name'): ['Undying'] * 20 + ['Riki'] * 20,
    ('player_4','kills'): range(3,43),
}
df = pd.DataFrame(data)
# df.melt(id_vars = [('player_1', 'name'), ('player_2', 'name'), ('player_3', 'name'), ('player_4', 'name')],
#         value_vars = [('player_1', 'kills'), ('player_2', 'kills'), ('player_3', 'kills'), ('player_4', 'kills')],
#         ignore_index=False)
df['Game'] = range(len(df))
df = df.melt(id_vars='Game', var_name = ['player', 'type'])
df = pd.merge(df.loc[df['type'] =='name', ['Game', 'player', 'value']], 
         df.loc[df['type'] =='kills', ['Game', 'player', 'value']], 
         on=['Game', 'player']).rename(columns={'value_x': 'name', 'value_y': 'kills'})
df.groupby('Game')
idx = df.groupby(['Game'])['kills'].transform(max) == df['kills']
print(df[idx])
Output:
     Game    player     name kills
120     0  player_4  Undying     3
121     1  player_4  Undying     4
122     2  player_4  Undying     5
123     3  player_4  Undying     6
124     4  player_4  Undying     7
125     5  player_4  Undying     8
126     6  player_4  Undying     9
127     7  player_4  Undying    10
128     8  player_4  Undying    11
129     9  player_4  Undying    12
130    10  player_4  Undying    13
131    11  player_4  Undying    14
132    12  player_4  Undying    15
133    13  player_4  Undying    16
134    14  player_4  Undying    17
135    15  player_4  Undying    18
136    16  player_4  Undying    19
137    17  player_4  Undying    20
138    18  player_4  Undying    21
139    19  player_4  Undying    22
140    20  player_4     Riki    23
141    21  player_4     Riki    24
142    22  player_4     Riki    25
143    23  player_4     Riki    26
144    24  player_4     Riki    27
145    25  player_4     Riki    28
146    26  player_4     Riki    29
147    27  player_4     Riki    30
148    28  player_4     Riki    31
149    29  player_4     Riki    32
150    30  player_4     Riki    33
151    31  player_4     Riki    34
152    32  player_4     Riki    35
153    33  player_4     Riki    36
154    34  player_4     Riki    37
155    35  player_4     Riki    38
156    36  player_4     Riki    39
157    37  player_4     Riki    40
158    38  player_4     Riki    41
159    39  player_4     Riki    42