Did you actually test that your regex would deal with spaces in the file name? I think not. \w+ will not match a space, only [0-9a-zA-Z_]. A demo of different regex:

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my %keepList;

while (my $line = <DATA>) 
{
   my $sdf_file;
   next unless ($sdf_file) = $line =~ /([\w ]+\.nfo)/;
   $keepList{$sdf_file} = 1;
   print "keeping \"$sdf_file\"\n"; #update for debugging #######
}

=example printout
keeping "filename1.nfo"
keeping "filename2.nfo"
keeping "file name2.nfo"
keeping "file name3.nfo"
keeping "file   name4.nfo"
=cut

__DATA__
fullpath="C:\directory\filename1.nfo"
id="1a"
fullpath="C:\directory\filename2.nfo"
id = "nonsense"
fullpath = "C:\directory\file name2.nfo"
fullpath = "C:/directory/file name3.nfo"
fullpath = "C:\directory/file   name4.nfo"
[download]

Your code:

my @files = $files;
opendir(OUTPUT, $files);
  @files = grep {$_ ne '.' and $_ ne '..'} readdir(OUTPUT);
closedir(OUTPUT);
[download]

better written? as:

opendir(OUTPUT, $files) or die "unable to opendir $!";
my @files = grep {-f $files/$_} readdir(OUTPUT);
closedir(OUTPUT);
[download]

The -f file test excludes not only the "." and ".." directories but also other ones that might exist.
my @files = $files; does nothing useful.

Overall, great job at getting something to "work". In the scheme of things, my comments are just nits.