The following will read everything into a dictionary keyed by player name. The value associated with each player is itself a dictionary acting as a record with named fields associated with the items converted to a format suitable for further processing.

info = {}
with open('scoring_info.txt') as input_file:
    for line in input_file:
        player, stats, outcome, date = (
            item.strip() for item in line.split('-', 3))
        stats = dict(zip(('kills', 'deaths', 'assists'),
                          map(int, stats.split('/'))))
        date = tuple(map(int, date.split('-')))
        info[player] = dict(zip(('stats', 'outcome', 'date'),
                                (stats, outcome, date)))

print('info:')
for player, record in info.items():
    print('  player %r:' % player)
    for field, value in record.items():
        print('    %s: %s' % (field, value))

# sample usage
player = 'Fizz'
print('\n%s had %s kills in the game' % (player, info[player]['stats']['kills']))

Output:

info:
  player 'Shyvana':
    date: (2012, 11, 22)
    outcome: Loss
    stats: {'assists': 5, 'kills': 12, 'deaths': 4}
  player 'Miss Fortune':
    date: (2012, 11, 22)
    outcome: Win
    stats: {'assists': 3, 'kills': 12, 'deaths': 4}
  player 'Fizz':
    date: (2012, 11, 22)
    outcome: Win
    stats: {'assists': 5, 'kills': 12, 'deaths': 4}

Fizz had 12 kills in the game

Alternatively, rather than holding most of the data in dictionaries, which can make nested-field access a little awkward — info[player]['stats']['kills'] — you could instead use a little more advanced "generic" class to hold them, which will let you write info2[player].stats.kills instead.

To illustrate, here's almost the same thing using a class I've named Struct because it's somewhat like the C language's struct data type:

class Struct(object):
    """ Generic container object """
    def __init__(self, **kwds): # keyword args define attribute names and values
        self.__dict__.update(**kwds)

info2 = {}
with open('scoring_info.txt') as input_file:
    for line in input_file:
        player, stats, outcome, date = (
            item.strip() for item in line.split('-', 3))
        stats = dict(zip(('kills', 'deaths', 'assists'),
                          map(int, stats.split('/'))))
        victory = (outcome.lower() == 'win') # change to boolean T/F
        date = dict(zip(('year','month','day'), map(int, date.split('-'))))
        info2[player] = Struct(champ_name=player, stats=Struct(**stats),
                               victory=victory, date=Struct(**date))
print('info2:')
for rec in info2.values():
    print('  player %r:' % rec.champ_name)
    print('    stats: kills=%s, deaths=%s, assists=%s' % (
          rec.stats.kills, rec.stats.deaths, rec.stats.assists))
    print('    victorious: %s' % rec.victory)
    print('    date: %d-%02d-%02d' % (rec.date.year, rec.date.month, rec.date.day))

# sample usage
player = 'Fizz'
print('\n%s had %s kills in the game' % (player, info2[player].stats.kills))

Output:

info2:
  player 'Shyvana':
    stats: kills=12, deaths=4, assists=5
    victorious: False
    date: 2012-11-22
  player 'Miss Fortune':
    stats: kills=12, deaths=4, assists=3
    victorious: True
    date: 2012-11-22
  player 'Fizz':
    stats: kills=12, deaths=4, assists=5
    victorious: True
    date: 2012-11-22

Fizz had 12 kills in the game