Greetings,
First some suggestions, against using barewords, and for using open in its three terms form: more explicit and understandable
Also I put there use autodie because I'm lazy :$

use warnings;
use strict;
use autodie;
open my $in,'<', "in.txt";
open my $out,'>', "out.txt";
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Since you start at first line and then jump over each line to save to the previous line you can use the perl auto variable for line counts

my $previous_line;

while (<$in>) {
    $current_line = $_;
    chomp $current_line;
    if(!defined($previous_line) || $. mod 2 != 0){
        $previous_line = $current_line;
        next;
    }
    my @previous_columns = split(" ", $previous_line);
    my $end_coor = $previous_columns[2] + $previous_columns[3];
    my @current_columns = split(" ", $current_line);
    my $seq_length = length $previous_columns[6];
    my $gap_count = $previous_columns[6] =~ tr/Q//;
    my $original_length = $seq_length - $gap_count;
    my $original_end_coor = $previous_columns[2] + $original_length;
    my $distance = $current_columns[2] - $original_end_coor;
    $current_columns[2] = $end_coor + $distance;
    $previous_line = $current_line;
    print $out "$current_columns[2]\n";
}

close $in;
close $out;
[download]

I'm not sure about the way you want to go over the file though, do you want to just jump over half of the lines?