Open the 2nd file and make a hash of the Gene to the column 2. Then read each line from file1, look up the gene's value in the hash, then add that to the end of the line from file1. It is not necessary to know how many columns are in file1 or even file2. Column 1 in file1 matters. Both Column 1 and Column2 in file2 matter.

#!/usr/bin/perl -w
use strict;

my %col2;  #gene in column 1 to special column 2

my ($file1, $file2) = @ARGV;
if (@ARGV != 2)
{
   print "some usage here\n"; exit();
};

open (my $two_cols, '<', $file2) or die "unable to open $file2 $!";
open (my $big_file, '<', $file1) or die "unable to open $file1 $!";

%col2 = map{   s/\s+$//; #chomp + zap trailing white space   
               my ($gene, $v) = split(/\t/,$_,3);
            }<$two_cols>;
            
while (<$big_file>)
{
   s/\s+$//;
   my ($gene, $rest) = split(/\t/,$_,2);
   if (my $lastcol = $col2{$gene})
   {
      print "$gene\t$rest\t$lastcol\n";
   }
   else
   {
      warn "$gene not found in $file2\n";  
   }
}

__END__
C:\TEMP>type f1.txt
gene1   1234    78975
gene13  9876    ldlgfjk

C:\TEMP>type f2.txt
gene1   abc
gene13  xyz

C:\TEMP>update.pl f1.txt f2.txt
gene1   1234    78975   abc
gene13  9876    ldlgfjk xyz
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