I think you'll get what you want if you change
my @reg= %{ ... };
to
my @reg= keys %{ ... };

Also, $Registry is already provided to you.

use strict; 
use warnings;

use Win32::TieRegistry;

my @reg = keys %{ $Registry->{"HKEY_CLASSES_ROOT\\batfile\\"} };

for ( @reg )
{
    print "$_\n";
}
[download]

outputs

DefaultIcon\
shell\
shellex\
\
\EditFlags
[download]