Not to belittle your efforts in any way, but IMHO your solution is far too complicated and hard to comprehend, and I believe this is because it tries to do too much. IMHO, the grouping function should be separate from any processing/analysis of the groups. If you simply return the groups to the caller, she can do whatever processing on them in her own way.

Here is how I would probably approach the problem:

sub find_groups(&\@)
{
    my( $keymap, $rows_ar ) = @_;
    my %groups;
    for ( @$rows_ar )
    {
        push @{ $groups{ &$keymap } }, $_;
    }
    \%groups
}
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Example: Show a count(*) of distinct values of the 'name' column:

my $groups_hr = find_groups { $_->{'name'} } @rows;

for my $k ( sort keys %$groups_hr )
{
    print "$k\t" . @{$groups_hr->{$k}} . "\n";
}
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Example: Group by a key consisting of multiple columns concatenated:

find_groups { join $;, @{$_}{qw( name game score )} } @rows;
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Example: Group by a key derived from the row by an arbitrarily complex function:

find_groups {
    $_->{'name'} eq 'foo' ? 1 :
    $_->{'game'} =~ /bar/ ? 2 :
    $_->{'score'} >= 500  ? 3 : 0
} @rows;
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Example: Find numeric mean within each group of the values in the 'score' field:

use List::Util qw( sum );

my $groups_hr = find_groups { $_->{'name'} } @rows;

for my $k ( sort keys %$groups_hr )
{
    my $avg = sum( map { $_->{'score'} } @{$groups_hr->{$k}} ) / @{$gr
+oups_hr->{$k}};
    print "$k\t$avg\n";
}
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Sure, you could argue that

    map { $_->{'score'} } @rows
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is an ugly way of extracting a column from a AoH table... but at least it's perlish. You could easily wrap that in a function if you wanted to.