I think its a bug like Bug #75644 for Regexp-Grammars: debug does not work

You can workaround by following http://search.cpan.org/src/DCONWAY/Regexp-Grammars-1.016/t/backref.t and http://search.cpan.org/src/DCONWAY/Regexp-Grammars-1.016/t/backref_ARG.t, which DO NOT test this (your) example from the docs

The workaround does work

#!/usr/bin/perl --
use strict;
use warnings;

use Data::Dumper;

my $grammar = do {
  use Regexp::Grammars;
  qr{
<debug:on>
<delimited_string>


<token: delimited_string>
    <delim=(['"`])> <content=(.*?)> <rdel=\delim>

}xms; };

my $string = "'hi'";
if ($string =~ $grammar) {
  print Dumper \%/;
}
__END__
=====> Trying <grammar> from position 0
'hi'   |...Trying <delimited_string>
       |   |...Trying <delim=(['"`])>
hi'    |   |    \_____<delim=(['"`])> matched '''
       |   |...Trying <content=(.*?)>
       |   |    \_____<content=(.*?)> matched ''
       |   |...Trying <rdel=\delim>
       |   |    \FAIL <rdel=\delim>
i'     |   |    \_____<content=(.*?)> matched 'h'
       |   |...Trying <rdel=\delim>
       |   |    \FAIL <rdel=\delim>
'      |   |    \_____<content=(.*?)> matched 'hi'
       |   |...Trying <rdel=\delim>
[eos]  |   |    \_____<rdel=\delim> matched '''
       |    \_____<delimited_string> matched ''hi''
        \_____<grammar> matched ''hi''
$VAR1 = {
          '' => '\'hi\'',
          'delimited_string' => {
                                  '' => '\'hi\'',
                                  'content' => 'hi',
                                  'delim' => '\'',
                                  'rdel' => '\''
                                }
        };
[download]

Regexp::Grammars::Common::String use this syntax

You should report this bug upstream , maybe write this example as a test case following t/backref*