I think you need to create the $treeout object with -file first so that it uses it as the stream for the write_tree method

my $outfile = 'C:\Users\AnyUser\Desktop\outree.tre';
my $treeout = Bio::TreeIO->new(
    -format => 'newick', 
    -file   => ">$outfile" );

while( my $aln = $alnio->next_aln ) 
{
  my $mat = $stats->distance(-method => 'Kimura',
                            -align  => $aln);
  my $tree = $dfactory->make_tree($mat);
  $treeout->write_tree($tree);
}
exit;
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