In your modified script, I hard coded the input and output file names as follows:

my $inputfile = 'Ath_orig.fa';
my $outputfile = 'Ath_tybalt_shuffle.fa';
[download]

the specified output file was created, BUT it was empty.

So I tried to modify your script very slightly to file handle syntax I am most familiar with, as follows, but here too the output file specified was empty. Not sure what I am doing wrong....

#!/usr/bin/perl
#tybalt89_DNAfreq_Random_Generator.pl

# https://perlmonks.org/?node_id=1228191

use strict;
use warnings;

my $window = 1e6;
my $A = my $C = my $G = my $all = 0;
my (@sizes, $tmp, $start);
my $in = shift @ARGV;
my $out = shift @ARGV;
print $in, "\n";
print $out, "\n";

open IN, '<', $in or die "$! opening $in";
open OUT, '>', $out or die "$! opening $out";

sub letter
  {
  my $n = int rand $all--;
  $n < $A ? ($A--, return 'a') :
    $n < $A + $C ? ($C--, return 'c') :
    $n < $A + $C + $G ? ($G--, return 'g') :
    return 't';
  }

sub output
  {
  for my $count ( @sizes )
    {
    print ">ID", $start++, "\n", map(letter(), 1 .. $count), "\n";
    print OUT ">ID", $start++, "\n", map(letter(), 1 .. $count), "\n";
    }
  @sizes = ();
  }

while( <IN> )
  {
  if( /^>/ )
    {
    $start //= s/\D+//gr;
    }
  elsif( /^[acgt]/ )
    {
    $A += tr/a//;
    $C += tr/c//;
    $G += tr/g//;
    $all += $tmp = tr/acgt//;
    push @sizes, $tmp;
    $all >= $window and output();
    }
  }
$all and output();
close IN;
close OUT;
[download]

Execution syntax was simply:

 perl tybalt89_DNAfreq_Random_Generator.pl Ath_orig.fa Ath_tybalt_shuffle.fa

Thanks a lot!