I had no problem to get something executable:

#!/usr/bin/perl
use strict;

use Data::Dumper;
my %hash = map { my $item = pop @$_; map { $_, $item } @$_ } 
 [qw(HELP ?) => sub { print "help\n"; }], 
 [qw(QUIT EXIT LEAVE) => sub { "exit"; }];

&{%hash->{HELP}}();
&{%hash->{'?'}}();
print Dumper(%hash);
1;
[download]

yields

help
help
$VAR1 = '?';
$VAR2 = sub { "DUMMY" };
$VAR3 = 'HELP';
$VAR4 = $VAR2;
$VAR5 = 'EXIT';
$VAR6 = sub { "DUMMY" };
$VAR7 = 'QUIT';
$VAR8 = $VAR6;
$VAR9 = 'LEAVE';
$VAR10 = $VAR6;
[download]

The [qw xxx],[qw xxx] are the list on which the first (leftmost) map operates.
For each [qw(X Y), anon_sub] the block of the leftmost map is executed and the result appended to the resulting hash.
In this block the last element is fetched in $item (my $item = pop @$_;) and then for each remaing element, which is the key, used as value in the resulting hash
(map { $_, $item } @$_)

HTH,
Tomte