I don't have access to a 64-bit perl. However, this is a 32-bit version of combining two 16 bit integers into a 32 bit number. While this runs as long as the coordinates are within range, I can't test it in the 64-bit version.

I like it because all offsets are found with a simple addition inside tick.
All the encode/decode mess is in the input and output routines.

In theory (completely untested), all that's needed is to change the line

my $half = 16; # make 32 for 64-bit perls
[download]

to

my $half = 32; # make 32 for 64-bit perls
[download]

to make it use the full range of two 32 bit numbers.

So here's the code

package Organism;

use strict;
use warnings;

sub count {
   return scalar keys %{ shift->{Cells} };
}

# Input a list of [ x, y ] coords
sub insert_cells {
   my $self = shift;
   my $cells = $self->{Cells};
   for my $r (@_) { $cells->{
    (($r->[0] + $self->{fudge}) << $self->{half}) |
    ($r->[1] + $self->{fudge})
    } = undef }
}

# Return sorted list of cells in the Organism.
# Used for verification and testing the state of the organism.
sub get_live_cells {
   my $self = shift;
   sort { $a->[0] <=> $b->[0] || $a->[1] <=> $b->[1] }
      map { [
      ($_ >> $self->{half}) - $self->{fudge},
      ($_ & (1 << $self->{half}) - 1) - $self->{fudge}
      ] } keys %{ $self->{Cells} };
}

sub tick {
   my $self  = shift;
   my $cells = $self->{Cells};
   my @deltas = @{ $self->{deltas} };
   my ( %new_cells, %dead_cells );

   for my $c (keys %{ $cells }) {
      # Get the (up to 8) dead cells surrounding the cell
      $dead_cells{$_}++ for my @zcells =
        grep !exists $cells->{$_}, map $c + $_, @deltas;

      # Check the live cell
      # Note: next line equivalent to nlive == 2 || nlive == 3
      @zcells == 5 || @zcells == 6 and $new_cells{$c} = undef;
   }
   $dead_cells{$_} == 3 and $new_cells{$_} = undef for keys %dead_cell
+s;
   $self->{Cells} = \%new_cells;
}

sub new {
   my $class = shift;
   my $half = 16; # make 32 for 64-bit perls
   my $base = 1 << $half;
   my $fudge = $base >> 1;
   my @deltas = ($base-1, $base, $base+1,
    -1, 1, -$base-1, -$base, -$base+1);
   my %init_self = ( Cells => {},
    fudge => $fudge, half => $half, deltas => \@deltas );
   bless \%init_self, $class;
}

1;
[download]

Preliminary testing with 16 bit numbers seemed to show it's about 10% slower than the pack version :(