In before everyone else suggests using a module for this. Path::Tiny is my current favorite module for general file bashing.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11124289
use warnings;
use Path::Tiny;

my $dirname = 'Filer';
my $outputfile = path('output.second.column');
$outputfile->spew(''); # empty file

for my $file ( path($dirname)->children( qr/\.txt\z/ ) )
  {
  $outputfile->append( map { (split /\t|\n/)[1] . "\n"} $file->lines )
+;
  }

# following for debug only :)
system 'more Filer/* output.second.column | cat';
# because 'more' shows filename and contents when piped
[download]

Outputs:

::::::::::::::
Filer/one.txt
::::::::::::::
one     two     three
four    five    six
::::::::::::::
Filer/three.txt
::::::::::::::
thirteen        fourteen        fifteen
sixteen seventeen       eighteen
::::::::::::::
Filer/two.txt
::::::::::::::
even    eight   nine
ten     eleven  twelve
::::::::::::::
output.second.column
::::::::::::::
two
five
fourteen
seventeen
eight
eleven
[download]

Is this the kind of thing you were looking for ?

P.S. See, it really is simple...