I disagree with it being a closure, even using the broader definition of a closure.

If you mean that a closure (in Perl) is anything that increases reference count anywhere, then I understand you, but must say that that's the broadest definition of a closure I've ever heard. With that definition though, this below would be equally much a closure:

    sub demonstration {
        return {
            demonstration_data => { demo_data => shift },
        };
    }
[download]

If you mean that it's a closure because you use a lexical variable in there, I disagree that it's a closure. Adding that it must close over/bind a lexical environment (which is what some people think and I think you are referring to), the returned hash reference is not a closure because it doesn't bind anything in its lexical surrounding.

$demonstration_data knows to stick around even though the function ended

In fact, it doesn't. The value it references knows to stay around. The instance of $demonstration_data doesn't stay around itself. Changing $demonstration_data after the latter hash reference is created does not change anything in it. This code below illustrates that.

    sub demonstration {
        my $demonstration_data = { demo_data => shift };
        return {
            demonstration_data => $demonstration_data,
        }, sub {
            $demonstration_data = $_[0];
        };
    }

    my ($data, $modifier) = demonstration('foo');

    print Dumper $data;
    $modifier->({ a => 1 });
    print Dumper $data;

    __END__
    $VAR1 = {
              'demonstration_data' => {
                                        'demo_data' => 'foo'
                                      }
            };
    $VAR1 = {
              'demonstration_data' => {
                                        'demo_data' => 'foo'
                                      }
            };
[download]

The hash value holds a RV that references the same PVHV as $demonstration_data references. $demonstration_data and demonstration()->{demonstration_data} are different RVs, but reference the same value.

One can argue that the reference operator \ can act as a closure. Looking at lexical variables, it binds the current instance of the lexical variable. The similarity between \ and an anonymous closure and the contrast to other scalar types is demonstrated below.

    sub foo {
        my $foo = shift;
        return
            $foo,
            [ $foo ],
            \$foo,
            sub :lvalue { $foo }
        ;
    }

    my ($noref, $aref, $sref, $cref) = foo('foo');

    my $dump = sub {
        print
            "\$noref: $noref\n",
            "\$aref : $aref->[0]\n",
            "\$sref : $$sref\n",
            "\$cref : " . $cref->() . "\n\n";
    };

    $dump->(); $noref     = 'bar'; # Changes the first value.
    $dump->(); $aref->[0] = 'baz'; # Changes the second value.
    $dump->(); $$sref     = 'zip'; # Changes the two last values.
    $dump->(); $cref->()  = 'zap'; # Changes the two last values.
    $dump->();

    __END__
    Long output, run it yourself.
[download]

Your hash above is no more closure than the array reference here. Neither the hash or the array bind the variables used in it - they store copies of the values the variables hold. In your case the value is a reference but that is no different from any other non-reference value except that it increases a ref count somewhere when copied, but that has nothing to do with closing over any environment.

One may argue that the array reference itself is a closure and so may be, if you look at [ LIST ] as syntactic sugar for do { my @foo = LIST; \@foo }. That does not make any data structure keeping a reference to the anonymous array a closure though. It's just a data structure that holds a closure.

ihb