Very nearly right. The assertion that '(' doesn't follow the link should be an assertion that '](' doesn't follow the link. Note that in the fixed code I've added a call to the sub so that the code runs as a complete sample:

use strict;
use warnings;

my $text = "Hello, I am a [Perl Monk], still not good at
[Regular Expressions]. I have been helped immensely
by the good monks at [Perl Monks](http://www.perlmonks.org).
This is what I look like ![mymugshot]. Thank you.";

listlink ($text);

sub listlink {
  my ($text) = @_;
 
  my @links = (
    $text =~ /
      (?<!\!\[) # make sure the match is not preceded by a ![
      (?<=\[)   # but is in fact preceded by just a [
      .*?       # the match
      (?=\])    # followed by a ]
      (?!\]\()    # but not followed by a (
    /xg
  );

  foreach my $link (@links) {
    print "$link\n";
  }
}
[download]

Prints:

Perl Monk
Regular Expressions
[download]