Not sure about the else branch. If my assumption of printing the unchanged data is correct, then there are further simplifications possible.

use strict;
use warnings;

my $threshold = 1000;

# being lazy:
my @file_array = map { [ split /\s+/ ] } <DATA>;

for( my $i=0; $i<@file_array-2; $i+=2 ) {
    if( $file_array[$i  ][3]-$file_array[$i+2][2] < $threshold and
        $file_array[$i+1][3]-$file_array[$i+3][2] < $threshold ) {
        print "$file_array[$i  ][0] $file_array[$i  ][2] $file_array[$
+i+2][3]\n"; 
        print "$file_array[$i+1][0] $file_array[$i+1][2] $file_array[$
+i+3][3]\n";
    } else {
        # not sure
        print "$file_array[$i  ][0] $file_array[$i  ][2] $file_array[$
+i  ][3]\n"; 
        print "$file_array[$i+1][0] $file_array[$i+1][2] $file_array[$
+i+1][3]\n";
    }
}
print "$file_array[-2][0] $file_array[-2][2] $file_array[-2][3]\n"; 
print "$file_array[-1][0] $file_array[-1][2] $file_array[-1][3]\n";

__DATA__
link1 myco1 16 13013 color=chr1
link1 myco2 7419028 7432025 color=chr1
link2 myco1 13016 31245 color=chr1
link2 myco2 7432026 7450255 color=chr1
link3 myco1 31569 50386 color=chr1
link3 myco2 7450876 7469693 color=chr1
link4 myco1 53241 82019 color=chr1
link4 myco2 7472518 7501295 color=chr1
link5 myco1 82667 85039 color=chr1
link5 myco2 7511397 7513769 color=chr1
link6 myco1 85052 162535 color=chr1
link6 myco2 7513770 7591243 color=chr1
link7 myco1 3519888 3527802 color=chr10
link7 myco2 6192981 6200895 color=chr10
link8 myco1 3531711 3535088 color=chr10
link8 myco2 6200982 6204356 color=chr10
link9 myco1 3537764 3568351 color=chr10
link9 myco2 6204393 6234981 color=chr10
link10 myco1 3585050 3670398 color=chr10
link10 myco2 6236328 6321680 color=chr10
[download]

nope sorry its not working its printing the same output but not merging the links i want the links to be merged

Then I still have not understood what you want to achieve. Which links are to be merged? Can you show what the desired output for this example would be? What is the threshold you are using?