if ($fi eq "\n") ## WRONG in this case
{
 exit;
}
[download]

The value of the variable $fi is not "\n" but an empty string, though in the script provided by the OP, if ($fi eq "\n") { .. still works. Note that "chomp", already removes "\n".
A simple test, shows this clearly like thus:

use warnings;
use strict;
use Test::More 'no_plan';

print "Please press enter to quit \n";
my $fi = <STDIN>;
chomp $fi;
  is $fi, "\n",'should fail';
if ( $fi eq "\n" ) {
    exit;
}
[download]

result shows this:

Please press enter to quit 
not ok 1 - should fail
#   Failed test 'should fail'
#   at textme.pl line 9.
#          got: ''
#     expected: '
# '
1..1
# Looks like you failed 1 test of 1.
[download]

If you look at the got and expected in the above, you get the point.